(vii) x is not irrational number but it is a square of an integer. r : the switch S3 is closed (xv) It rains heavily. [(~ p q) (~ r)] [(q p) (~ s r)] Solution: (v) [(~p q) (q r)] (p r) CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. The truth values of both p and q are F. (B) T, F All the entries in the last column of the above truth table are F. q : Triangle is isosceles. r : the switch S3 is closed Then, the symbolic form of the given switching circuit is : [p (~ q) (~ r)] [p (q r)] They will learn about Statements, Statement Patterns, Duals, Negations, etc., and much more. (v) If ABC is right angled at B, then mA + mC = 90. (xiii) x2 6x 7 = 0, when x = 7. It is an imperative sentence, hence it is not a statement. ~ (p q) (~ r) (Negation of conjunction) Maharashtra State Board 12th Maths Solutions Chapter 1 Mathematical Logic Miscellaneous Exercise 1. Write the symbolic form of the following switching circuit construct its switching table and interpret it. ~ p T (Complement Law) Nagpur is in Maharashtra and Chennai is in Tamil Nadu. (iii) ~(p q) (~p q) ~p Solution: n N, n2 + n is even number while n2 n is an odd number. (xii) Can you speak in Marathi ? False, (iii) x A, such that x + 7 11. the truth value of p q is T. [T T T], (vii) 24 is a composite number or 17 is a prime number. Mathematics is a subject which can be difficult for some students and easy for others. ~ p : the switch S1 is closed or the switch S1 is open What is the truth value of a statement? T F F (xv) It rains heavily. It is a statement which is true, hence its truth value is T. GET 1 FREE CLASS & 1 FREE WEEK OF CLUB ACCESS. All the entries in the last column of the above truth table are T. (p q) (r s) (T T) (F F) Solution: (viii) A quadratic equation cannot have more than two roots. [p (q r)] [(p q) r] is a tautology. (p q) (~p) (p ~q). (B) ~(p q) (p q) n N, 11 + 6 > 8 is a false statement, hence its truth value is F. True, (ii) x A, x + 5 < 12. Application of Logic to Switching Circuits Multiple Choice Questions for . It f(2) = 0 then f(x) is divisible by (x 2). The negation of (p q) (q ~ r) is (p ~p q) (~p q r) (p q r) y (p ~q r) (By Commutative Law) Solution: [(F T) T] [T (T F)] Solution : The truth values of p and q are F and T respectively. link here. Search for: Recent Posts. Using the truth table proves the following logical equivalence. If A = {1, 2, 3, 4, 5} then which of the following is not true? (vii) If A = {1, 2, 3, 4, 5} then which of the following is not true? Using the Mathematical Logic Class 12 Solutions, students can practice and will soon be able to answer questions related to the chapter. Solution: (i) Tirupati is in Andhra Pradesh. It is a statement which is true, hence its truth value is T. Let p : 24 is a composite number. (~p q r) (p q r) (p ~q r) (By Identity Law) Chapter 1 Mathematical Logic Ex 1.1 . p (q r) T (T F) (i) p (q r) Using the rule of negation write the negation of the following with justification. All the entries in the last column of the above truth table are T. Question 5. This is your chance to download the Maharashtra Board 12th Maths Solutions Chapter 1 Mathematical Logic ex 1.1. (p ~q) (~p q) (~p ~ q) (b) T, F, (v) The negation of inverse of ~p q is ________. n N, such that n + 5 > 10 is a true statement, hence its truth value is T. The truth values of p and q are T and F respectively. (iv) Angle is neither acute nor obtuse. Then the symbolic form of the given statement is : (p q) (p r). Solution: [(p (p q)] q is a tautology. It is a statement which is true, hence its truth value is T. Using the rules in logic, write the negations of the following : (~ q) (~ p r) (Distributive Law), (ii) p (q r) Let p : The angle is right angle. Solution: the truth value of p q is F. [T F F]. Students should read the 12th Board Exam Mathematics and Statistics Syllabus to learn about the subject's subjects and subtopics. A family becomes literate if the woman in it is literate. The entries in the columns 5 and 7 are identical. (A) Solution: Question 4. Hence the truth value of the given statement is false. State which of the following sentences are statements. Check whether the following switching circuits are logically equivalent Justify. (p q) (p r) and p (q r) Solution: Simplify the following so that the new circuit circuit. Construct the truth table for each of the following : It is an open sentence. Solution: Write converse, inverse and contrapositive of the following statement. Then the symbolic form of the given statement is ~ p. Then the symbolic form of the given statement is pq. q : the switch S2 is closed ~(p ~q) ~(q ~p) p q (Negation of disjunction) The chapter introduces the students to different logical concepts that are used to solve mathematical problems. Solution: So, this sentence can be either true or false. Solution: [T (q r)] (p ~q r) = (q r) (p ~q r) (By Complement Law) Solution : ~ p : the switch S1 is closed or the switch S1 is open that can be asked in the final exam. Let p : Milk is white. Solution: ~p (~q ~r) (Negation of disjunction), (iii) (p q) r 3 is a root of the equation x2 + 3x 18 = 0. q : The cube of any odd number is odd. Solution: This will clear students doubts about any question and improve application skills while preparing for board exams. the truth value of p v q is F. [F F = F], (ii) 64 is a perfect square and 46 is a prime number. [(~p p) (q ~q)] (p q) (By Commutative Law) (b) p q. (ii) x 3 = 14. (p q p) ( p q r) (p q r). [(~ p q) (~ r)] [(q p) (~ s r)] i) If p q is false and p q is true, the ________ is not true. It is a statement which is true, hence its truth value is T. Every single solution has been explained in a step-by-step manner by the learned subject matter experts at Vedantu. (p q) (q p) is a tautology. q : It is of measure 90. (vi) (p q) (~p q) (p ~q) (~p ~q) Which of the following sentences are statements in logic? The experts at Vedantu have taken special care to provide these important exercise solutions from the chapter to ensure that students are able to score high marks in their Class 12 board examination. ~ [(~T F) (F ~T)] (T F) the alternative arrangement of the new circuit with minimum switches is : Question 16. Using the laws of logic, we have, Solution: (C) (~p ~q) ~r (A) p (q r) (q p) r (By Identity Law) ~p ~q. The truth values of p is F. Solution: (p q) (p ~q) is a contradiction. Mathematical logic also talks about the truth value of a particular statement and how to find it out. Select and write the correct answer from the given alternatives in each of the following questions : Let p : the switch S1 is closed Solution: (xi) All real numbers are whole numbers. (F F) F (F F) F It is an open sentence, hence it is not a statement. = [(p q) ~(r s t)] [(p q) (r s t)] (By De Morgans Law) Solution: Since p q and p q both are T, from the table the truth values of both p and q are T. (ii) (p q) is T and (p q) q is F If A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, determine the truth value of the following statement: Construct the truth table of the following: Determine whether the following statement pattern is a tautology, contradiction, or contingency: Determine whether the following statement pattern is a tautology, contradiction or contingency: (p q) (p q) (p q) (p q). (~p q p ~q) (p q) From the table, the final column and the column of p are identical. Let p : 3 5 = 8. ~p : the switch S1 is closed, or the switch S1 is open Solution: Write the following compound statement symbolically. ~ [(~p q) (p ~q)] Solution: = (p q) F (By Complement Law) Question 2. Solution: The truth values of p and q are T and F respectively. Solution: [(~T T) (~F)] [(T T) (~F F)] Also, draw the simplified circuit. x A, x + 9 > 15. Then the symbolic form of the given statement is RS Aggarwal Class 12 is the most simplified book for Maharashtra state board Mathematics preparation amongst Class 12 students. [(p q) ~r ~s ~t] [(p q) (r s t)] Using rules of negation write the negations of the following with justification. Solution: Question 15. All the entries in the last column of the above truth table are T. Question 3. Solution: ~p q (Commutative Law) Prepare the switching table : Also, draw the simplified circuit. q : Chennai is in Tamil Nadu. . If ABC is right-angled at B, then mA + mC = 90. Hence the truth value of the given statement is false. It is a statement which is true, hence its truth value is T. ~ [(p q) (q ~r)] In ABC if all sides are equal then its all angles are equal. link here. (v) [(p (p q)] q (ii) (p q) (r s) Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Author: Balbharati Publisher: Maharashtra State Bureau of Textbook Production and Curriculum Research Language: . Let p : Angle is acute. Represent the following switching circuit in symbolic form and construct its switching table. (i) 4 is odd or 1 is prime. It is a statement which is true, hence its truth value is T. Solution: A total of 15 chapters that are prescribed by Class 12 Mathematics textbooks are included in a stepwise logical manner and answers are also given to the unsolved exercises. Then the symbolic form of the given statement is Pq. It is an interrogative sentence, hence it is not a statement. For Bill Ackerman '64. (iii) Close the door. = (p ~p) (~q ~p) (By Distributive Law) (v) (~r p) (~q) Let p : the switch S1 is closed In this chapter, students will be able to learn how to identify statements using logic. Let p : 5 is a prime number. The square of any even number is odd or the cube of any odd number is odd. Yes, the statement Zero is a complex number is in fact true and its truth value is T. 5. Let p : ABC is right angled at B. Solution: The Mathematics Part I course is delivered in Marathi. ~ [(p q) r] (A) ~p (~q ~r) (ii) Let p : the switch S1 is closed Imperial (13) 940 Main Street, Suite 202 El Centro, CA 92243 (760) 482-4226 Polling Place Locations. Solution: r : the switch S3 is closed It is a statement which is false, hence its truth value is F. Solution: Sun 8/29/2021 5:30 PM. Solution: = 24. Mathematical Logic is a fundamental unit of Mathematics in the Class 12 Maharashtra Board. Maharashtra State Board 12th Maths Solutions Chapter 1 Mathematical Logic Ex 1.1 Question 1. (i) [(p q) ~q)] ~p A quadratic equation cannot have more than two roots. It is an interrogative sentence, hence it is not a statement. #class12thmaths#chapter1mathematicallogic#mathematicallogic#Exercise1.1#maharashtrastateboard #udexyclasses#apekshaLecture 2 linkhttps://youtu.be/O4K35WUB0Qc. Solution: (p ~q) (~p q) (~p ~q) It is an interrogative sentence, hence it is not a statement. Select and write the correct answer from the given alternatives in each of the following questions : It 2 is a rational number then `sqrt2` is irrational number. [(p q) ~q)] ~p is a tautology. Further in the chapter, students will also learn how to find negation and dual of any particular statement pattern. OR n A, such that n + 7 6. F (~p q r) (p q r) (p ~q r) (By Identity Law) Solution: (ii) 3 is not a root of the equation x2 + 3x 18 = 0. Hence the truth value of the given statement is false. (a) q p, (vi) The negation of p (q r) is ________. [~T (~T F)] [(T F) V (T F)] the simplified form of the given circuit is : Maharashtra State Board Class 12 Solutions, Maharashtra State Board Class 11 Solutions, Maharashtra State Board Class 10 Solutions, Maharashtra State Board Class 9 Solutions, Maharashtra State Board Class 8 Solutions, Maharashtra State Board Class 7 Solutions, Maharashtra State Board Class 6 Solutions, Maharashtra State Board Class 5 Solutions, 12th Maharashtra State Board Maths Solutions Book, Maharashtra Board 12th Maths Solutions Chapter 1 Mathematical Logic Ex 1.5, Maharashtra Board 12th Maths Solutions Chapter 2 Matrices Ex 2.1, Maharashtra State Board Book Keeping and Accountancy 11th Solutions Digest | 11th Class Accounts Book Solution, Maharashtra State Board Class 11 Economics Solutions Digest, Maharashtra State Board Class 11 Political Science Solutions Digest, Maharashtra State Board Class 11 History Solutions Digest, Maharashtra State Board Class 5 Maths Solutions, Maharashtra State Board Class 5 Environmental Studies Solutions EVS Part 1 & 2, Maharashtra State Board Class 11 Information Technology IT Solutions Digest (Commerce, Science, Arts), Maharashtra State Board Yuvakbharati English 12th Digest Guide Textbook Answers, Maharashtra State Board Class 12 Political Science Solutions Digest, Maharashtra State Board Class 9 Maths Solutions Digest Part 1 & 2, Maharashtra State Board Class 12 Psychology Solutions Digest. Inverse of statement pattern (p q) (p q) is ________ . F F F ~ [(~T F) (F ~T)] (T F) Since the truth values of (p q) is F and (p q) q is T, from the table, the truth values of p and q are either T and F respectively or F and T respectively or both F. Question 9. ~ q: the switch S2 is closed or the switch S2 is open. q : n N, n2 n is an odd number. T T T Hence the truth value of the given statement is false. Get the free view of chapter 1 Mathematical Logic 12th Board Exam extra questions for Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board and can use Shaalaa.com to keep it handy for your exam preparation, Miscellaneous Exercise 1 | Q 1.1 | Page 32, Miscellaneous Exercise 1 | Q 1.2 | Page 32, Miscellaneous Exercise 1 | Q 1.3 | Page 32, Miscellaneous Exercise 1 | Q 1.4 | Page 32, Miscellaneous Exercise 1 | Q 1.5 | Page 32, Miscellaneous Exercise 1 | Q 1.6 | Page 32, Miscellaneous Exercise 1 | Q 1.7 | Page 32, Miscellaneous Exercise 1 | Q 2.1 | Page 33, Miscellaneous Exercise 1 | Q 2.2 | Page 33, Miscellaneous Exercise 1 | Q 2.3 | Page 33, Miscellaneous Exercise 1 | Q 2.4 | Page 33, Miscellaneous Exercise 1 | Q 2.5 | Page 33, Miscellaneous Exercise 1 | Q 2.6 | Page 33, Miscellaneous Exercise 1 | Q 3.1 | Page 33, Miscellaneous Exercise 1 | Q 3.2 | Page 33, Miscellaneous Exercise 1 | Q 3.3 | Page 33, Miscellaneous Exercise 1 | Q 3.4 | Page 33, Miscellaneous Exercise 1 | Q 3.5 | Page 33, Miscellaneous Exercise 1 | Q 3.6 | Page 33, Miscellaneous Exercise 1 | Q 4.1 | Page 33, Miscellaneous Exercise 1 | Q 4.2 | Page 33, Miscellaneous Exercise 1 | Q 4.3 | Page 33, Miscellaneous Exercise 1 | Q 4.4 | Page 33, Miscellaneous Exercise 1 | Q 5.1 | Page 33, Miscellaneous Exercise 1 | Q 5.2 | Page 33, Miscellaneous Exercise 1 | Q 5.3 | Page 33, Miscellaneous Exercise 1 | Q 6.1 | Page 33, Miscellaneous Exercise 1 | Q 6.2 | Page 33, Miscellaneous Exercise 1 | Q 6.3 | Page 33, Miscellaneous Exercise 1 | Q 6.4 | Page 33, Miscellaneous Exercise 1 | Q 6.5 | Page 33, Miscellaneous Exercise 1 | Q 7.1 | Page 33, Miscellaneous Exercise 1 | Q 7.2 | Page 33, Miscellaneous Exercise 1 | Q 7.3 | Page 33, Miscellaneous Exercise 1 | Q 7.4 | Page 33, Miscellaneous Exercise 1 | Q 7.5 | Page 33, Miscellaneous Exercise 1 | Q 7.6 | Page 33, Miscellaneous Exercise 1 | Q 7.7 | Page 33, Miscellaneous Exercise 1 | Q 7.8 | Page 33, Miscellaneous Exercise 1 | Q 8.1 | Page 34, Miscellaneous Exercise 1 | Q 8.2 | Page 34, Miscellaneous Exercise 1 | Q 8.3 | Page 34, Miscellaneous Exercise 1 | Q 9.1 | Page 34, Miscellaneous Exercise 1 | Q 9.2 | Page 34, Miscellaneous Exercise 1 | Q 10.1 | Page 34, Miscellaneous Exercise 1 | Q 10.2 | Page 34, Miscellaneous Exercise 1 | Q 10.3 | Page 34, Miscellaneous Exercise 1 | Q 11.1 | Page 34, Miscellaneous Exercise 1 | Q 11.2 | Page 34, Miscellaneous Exercise 1 | Q 11.3 | Page 34, Miscellaneous Exercise 1 | Q 11.4 | Page 34, Miscellaneous Exercise 1 | Q 12.1 | Page 34, Miscellaneous Exercise 1 | Q 12.2 | Page 34, Miscellaneous Exercise 1 | Q 13.1 | Page 34, Miscellaneous Exercise 1 | Q 13.2 | Page 34, Miscellaneous Exercise 1 | Q 14.1 | Page 35, Miscellaneous Exercise 1 | Q 14.2 | Page 35, Miscellaneous Exercise 1 | Q 15 | Page 35, Miscellaneous Exercise 1 | Q 16 | Page 35, Miscellaneous Exercise 1 | Q 17 | Page 35, HSC Arts (Marathi Medium) Mathematics and Statistics, HSC Science (Computer Science) Mathematics and Statistics, HSC Science (Electronics) Mathematics and Statistics, HSC Science (General) Mathematics and Statistics, Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board, Maharashtra Board Question Bank with Solutions (Official), Mumbai University Engineering Study Material, CBSE Previous Year Question Paper With Solution for Class 12 Arts, CBSE Previous Year Question Paper With Solution for Class 12 Commerce, CBSE Previous Year Question Paper With Solution for Class 12 Science, CBSE Previous Year Question Paper With Solution for Class 10, Maharashtra State Board Previous Year Question Paper With Solution for Class 12 Arts, Maharashtra State Board Previous Year Question Paper With Solution for Class 12 Commerce, Maharashtra State Board Previous Year Question Paper With Solution for Class 12 Science, Maharashtra State Board Previous Year Question Paper With Solution for Class 10, CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 12 Arts, CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 12 Commerce, CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 12 Science, CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 10, HSC Science (General) 12th Board Exam Maharashtra State Board, HSC Arts 12th Board Exam Maharashtra State Board, HSC Science (Electronics) 12th Board Exam Maharashtra State Board, HSC Science (Computer Science) 12th Board Exam Maharashtra State Board. Solution: [~p (~q r)(q r)(p r)] (~p ~q) [~q ~(~r)] (Negation of disjunction) No, the sentence is an Order, and hence it cannot be a statement. T F T 12th Standard, HSC Maharashtra State Board, Chapter 1 - Mathematical Logic, [Latest edition], . (i) 4! Write the following compound statements symbolically: Question 1. Humboldt (12) 2426 6th Street Eureka, CA 95501 (707) 445-7481 Polling Place. Question 5. Balbharti 12th Maharashtra State Board Maths Solutions Book Pdf Chapter 1 Mathematical Logic Ex 1.4 Questions and Answers. Determine the truth values of p and q in the following case: Using the truth table, prove the following logical equivalence : Using truth table, prove the following logical equivalence : Using rules in logic, prove the following: Using the rules in logic, write the negation of the following: Express the following circuit in the symbolic form. (ii) ~p q (p q) ~p 2. Solution: (iii) Some triangles are equilateral triangle. n A, such that n + 7 6. (i) Solution: Let p : the switch S . This will help in improving the overall understanding of the chapter students. (iii) (q r) (~p s) So, it is not necessary to use any switch in the circuit. They will be familiarized with the concept of creating truth tables and examining the logical equivalence of certain statement patterns. The chapter introduces the students to different logical concepts that are used to solve mathematical problems. ], (iii) Inverse of statement pattern (p q) (p q) is ________. HSC Maharashtra State Board, Chapter 1 - Mathematical Logic, [Latest edition], Balbharati solutions, for Mathematics and Statistics 1 (Commerce) . (iii) India is a country and Himalayas is a river. If the truth value of p is T, then the truth value of q is T. It is a statement which is false, hence its truth value is F. Let p : 5 3i is a real number. q : Its all angles are equal. (ix) Do you like Mathematics ? The negation of inverse of p q is ________. Solution: The truth values of p and q are T and F respectively. Solution: (D) ~q ~p It is not true that 53i is a real number. Write down the truth All the entries in the last column of the above truth table are T. Solution: Solution: Statements - Introduction, sentences and statement, truth value of statement, open sentences, compound statement, quantifier and quantified statements, logical connectives : conjunction, disjunction, negation, implication . = ~p ~p (By Commutative Law) Comprehensive Course on Mathematics - HSC, Class XII. (i) 4 is odd or 1 is prime. The truth values of both p and q are F. the truth values of ~ p is T. [~ F T], (v) If 3 5 = 8, then 3 + 5 = 15. Solution: r : the switch S3 is closed Determine whether the following statement patterns are tautologies contradictions or contingencies : Solution: students that are preparing for their exams. Solution: (vi) Hima Das wins gold medal if and only if she runs fast. Since the truth values of (p q) is T and (p q) q is F, from the table, the truth values of p and q are T and F respectively. Justify. T (By Identity Law) By Distributive Law, p (q r) (p q) (p r) Hima Das wins gold medal if and only if she runs fast. Then the symbolic form of the given statement is p q Using the laws of logic, we have, State which of the following sentences are statements. It is a statement which is true, hence its truth value is T. Select and write the correct answer from the given alternative of the following question: If p q is false and p q is true, then __________ is not true. Solution: Solution: ~ p (Identity Law) (ii) Triangle is equilateral or isosceles, T F F Solution: Then the symbolic form of the given statement is ~ p. (ii) x 3 = 14. Then the symbolic form of the given statement is pq. Apart from that, students will be able to learn how to combine two or more statements using logic. (p q) r is logically equivalent to ________ . It is an open sentence, hence it is not a statement. (c) x A, x + 6 9. p (q r) and (p q) (p r) respectively. t : the switch S5 is closed Question 4. It is a statement which is true, hence its truth value is T. Let p : Milk is white. (iv) Angle is neither acute nor obtuse. Balbharti 12th Maharashtra State Board Maths Solutions Book Pdf Chapter 1 Mathematical Logic Ex 1.4 Questions and Answers. (ii) (p q) r is logically equivalent to ________. 12th Maharashtra State Board Maths Solutions Book Pdf Part 1 12th State Board Maths Solution Book Pdf Download English Medium Chapter 1 Mathematical Logic Chapter 1 Mathematical Logic Ex 1.1 Chapter 1 Mathematical Logic Ex 1.2 Chapter 1 Mathematical Logic Ex 1.3 Chapter 1 Mathematical Logic Ex 1.4 Chapter 1 Mathematical Logic Ex 1.5 ~(p q) (~p q) ~p. Solution: q : She runs fast. Question 5. Solution: (iv) [(p q) r] [~r (p q)] ~ q: the switch S2 is closed or the switch S2 is open. (iii) The angle is right angle if and only if it is of measure 90. Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Solution: Quadrilateral is a square if and only if it is a rhombus. Maximum students of Maharashtra State Board 12th Board Exam prefer Balbharati Textbook Solutions to score more in exam. Justify. (ii) x A, such that x + 9 15. The negations of the given statements are : this is the first video of new syllabus class 12th maharashtra port and in this video, we have discuss about the definition of statement, the truth value of the statement, types of sentences,. Then the symbolic form of the given statement is p q. (A) x A such that x + 3 = 8 (i) n A, n + 7 > 6. (F q) (~p q r) (p q r) (p ~q r) (By Complement Law) It is a statement which is false, hence its truth value is F. (iii) \(\sqrt {2}\) is a rational number. Solution: Welcome to The 12 Gym! Reunion Cruise. These solutions are extremely important for the students since they can develop a good understanding of the chapter from these study materials. Solution: Determine the truth values ofp and q in the following cases : Inyo (14) 168 North Edwards Independence, CA 93526 (760) 878-0224 Polling Place Look-up . Let p : Hima Das wins gold medal (v) In ABC if all sides are equal then its all angles are equal. To provide a more comprehensive idea about the chapter, the experts at Vedantu have formulated some solutions for the exercise questions in the chapter. q ~ p (Identity Law) Let p : 24 is a composite number. Discuss the statement pattern, using truth table : ~(~p ~q) v q, Examine whether the following logical statement pattern is a tautology, contradiction, or contingency. ~p q (p q) ~p. Let p : Triangle is equilateral. 3. (B) (p q) ~r [~p (~q r)(q r)(p r)] (p q) r p (q r). apter. Mathematical logic is a chapter of huge significance for Class 12 Maharashtra Board students that are preparing for their exams. Write the truth values of the following statements : Solution: Construct the switching circuit of the following: Give an alternative equivalent simple circuit for the following circuit: find the symbolic fom of the following switching circuit,construct its switching table and interpret it. Then the symbolic form of the given statement is pq. Students can practice the exercises of the chapter and refer to these solutions to answer questions in their examination. Hence the truth value of the given statement is true. (vii) [(p ~q) (~p q)] r Let p : Nagpur is in Maharashtra. Express the following circuit in the symbolic form of logic and writ the input-output table. Check whether the following switching circuits are logically equivalent - Justify. ~ [p (q r)] It is an imperative sentence, hence it is not a statement. Solution: (B) Justify your answer. Then the symbolic form of the given statement is Pq. Then the symbolic form of the given statement is p q. (i) Tirupati is in Andhra Pradesh. Maharashtra State Board 12th Maths Solutions Chapter 1 Mathematical Logic Ex 1.4. The questions involved in Balbharati Solutions are important questions Using truth tables prove the following logical equivalences : 12th State Board Maths Solution Book Pdf English Medium Chapter 8 Binomial Distribution . In case students have some doubts regarding the chapter, they can always refer to the Mathematical Logic Class 12 PDF Maharashtra Board solutions in order to cross-check the answers and rectify their mistakes. Write your conclusion from the switching table. \(\sqrt {2}\) is not a rational number. (iv) (p q) (~ r) Using rules of negation write the negations of the following with justification. It begins as members enter the state-of-the-art group room . Solution: (iv) The square of any even number is odd or the cube of any odd number is odd. = (p ~q) (~p T) (By Complement Law) The textbook recommended by the Maharashtra Board is "Yuvabharati". the truth value of p v q is F. [F F = F], (ii) 64 is a perfect square and 46 is a prime number. Hence the truth value of the given statement is true. = (p q) [ ~(r s t) (r s t)] (By Distributive Law) (~r p) (~q) (~F T) (~T) Hence the truth value of the given statement is true. Solution: (ii) is an irrational number. . [q p) ((q ~q)] r (By Distributive Law) Let p : 3 5 = 8. Construct the truth table of the following statement pattern. Concepts covered in Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board chapter 1 Mathematical Logic are Concept of Statements, Truth Value of Statement, Logical Connective, Simple and Compound Statements, Statement Patterns and Logical Equivalence, Tautology, Contradiction, and Contingency, Duality, Quantifier and Quantified Statements in Logic, Negations of Compound Statements, Converse, Inverse, and Contrapositive, Algebra of Statements, Application of Logic to Switching Circuits. Milk is white if and only if sky is blue. [(F T) T] [T (T F)] [(~p p) (q r)] (p ~q r) (By Distributive Law) Solution: x is not irrational number but is a square of an integer. Solution: (a) p (q r) [Hint: Use truth table. (iii) (p q) is F and (p q) q is T Download the notes and solutions now to gather more information about the chapter. q : Triangle is isosceles. (i) Nagpur is in Maharashtra and Chennai is in Tamil Nadu. = (p ~q) ~ p (By Identity Law) (v) Please get me breakfast. It is a statement which is true, hence its truth value is T. (~q ~p) (~q r) (Commutative law) In case of a statement, state its truth value. Solution: Using the laws of logic, we have, Balbharti 12th Maharashtra State Board Maths Solutions Book Pdf Chapter 1 Mathematical Logic Ex 1.1 Questions and Answers. 64 is a perfect square and 46 is a prime number. Then the symbolic form of the given statement is p q. F F F (vii) x2 = x. Let p : the switch S1 is closed Solution: Solution: (p q ~p) (~p q r) (p q r) (p ~q r) Solution: Solution: Solution: Then the symbolic form of the given statement is pq. Maharashtra State Board 12th Maths Solutions Chapter 1 Mathematical Logic Ex 1.1. Solution: in order to cross-check the answers and rectify their mistakes. Question 1. Let p : 4 is odd. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster. q : the switch S2 is closed . Write the following compound statements symbolically: Thus, building a strong conceptual foundation becomes a lot easier by taking help from the Differential Calculus JEE Advanced questions. By the rules of negation of biconditional, T T T Solution: Solution : Balbharti 12th Maharashtra State Board Maths Solutions Book Pdf Chapter 1 Mathematical Logic Ex 1.1 Questions and Answers. Solution: It is a statement which is true, hence its truth value is T. Solution: ~q : the switch S2 is closed or the switch S2 is open. Note : If p : x is irrational number, then the symbolic form of the given statement is ~p q. In the case of the statement, write down the truth value : Question 2. [F (F F)] [F V F] Hence the truth value of the given statement is false. It is a statement which is true, hence its truth value is T. (i) x A such that x + 8 = 15. In case of statement, write down the truth value : Using truth table, prove that ~ p q (p q) ~ p. Using the truth table prove the following logical equivalence. BURN WED. link here. Maharashtra State . (C) ~p (~q ~r) F T T Maharashtra State Board 12th Maths Solutions Chapter 1 Mathematical Logic Ex 1.4. (viii) (p q) (q p) In case the statement is true, the truth value will be T. 4. 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It is a statement which is false, hence its truth value is F. Solution: Maharashtra Board Class 12 Solutions for Maths Chapter 1 Mathematical Logic - PDF will be uploaded soon. ENROLL. It is a statement which is true, hence its truth value is T. Justify your answer if it is a statement. Pawan Kumar. ~ [(F F) (F F)] F Represent the following switching circuit in symbolic form and construct its switching table. (c) (~p ~q) (~p ~ q), (iv) If p q is F, p q is F then the truth values of p and q are ________. There are solved questions and examples provided in the chapter that will help students perfect their answers and get their doubts cleared. Draw the corresponding switching circuit. q : 7 divides 94. Solution: Hence, the given circuit is equivalent to the simple circuit with only one switch S1. Then the symbolic form of the given statement is pq. Logic Ex 1.5 covered by this Book Logic also talks about the introduces! 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