Mathematical Reasoning Class 11 OP Malhotra Exe-27D ISC Maths Ch-27 Solutions. In this article you would learn about Truth Table For A Negation. Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics.

Mathematical Reasoning Class 11 OP Malhotra Exe-27D ISC Maths Solutions Ch-27

Board	ISC
Publications	S Chand
Subject	Maths
Class	11th
Chapter-27	Mathematical Reasoning
Writer	O.P. Malhotra
Exe-27(D)	Truth Table For A Negation

Truth Table For A Negation.

Mathematical Reasoning Class 11 OP Malhotra Exe-27D ISC Maths Ch-27 Solutions.

Que-1: Let p, q, r and s represent simple statements. Assume that p is false, q is true, r is false, and s is true. Determine the truth value of each statement expressed below :
(i) q ∧ r     (ii) r ∨ p       (iii) p ∧ S       (iv) p ∨ s     (v) ~q      (vi) q ∨ s     (vii) ~ r      (viii) s ∧ q    (ix) r ∧ p

Sol: Given p is false, q is true, r is false and s is true.
(i) The truth value of statement is false as one of the component statement is false.
(ii) The truth value of statement is false since both component statements are false.
(iii) The truth value of compound statement is false since one of the component statement is false.
(iv) The truth value of compound statement is true since one of the component statement is true.
(v) The truth value of statement is false,
(vi) The truth value of q ∨ s is true since both component statements are true.
(vii) The truth value of compound statement is true.
(viii) The compound statement has truth value is true.
since, both component statements are true.
(ix) The truth value of compound statement is false.
since both component statements are false.

Que-2: Let a, b, c and d represent simple statements. Assume that a ∧ d is true, b ∧ C is false, and ~ c is false.
(i) What is the truth value of a?
(ii) What is the truth value of d?
(iii) What is truth value of c?
(iv) What is the truth value of b?

Sol: Given a ∧ d is true ⇒ a and d both statements are true.
and b ∧ C is false. …(1)
Since ~ c is false ⇒ c is true
∴ from (1); b is false (∵ F A T = F)
(i) The truth value of a be true.
(ii) The truth value of d be true.
(iii) The truth value of c be true.
(iv) The truth value of b be false.

Que-3: Assume that two given statements p and q are both true and indicate whether or not you would expect each of the following statements to be true :
(i) P ∧ q        (ii) p ∨ q        (iii) p ∨ (~q)     (iv) (~p) ∨ (~ q)

Sol: Given statements p and q are both true.
(i) Thus, the statement p ∧ q = T ∧ I = T is also true.
(ii) The statement p ∨ q is also statement.
(iii) p ∨ (~ q) = T ∨ F = T
(iv) (~p) ∨ (~ q) = F ∨ F = F

Construct truth tables for :

Que-4: (~p) ∧ q

Sol: 

Que-5: (~p) ∧ (~q)

Sol: 

Que-6: ~(p ∧ q)

Sol: The truth table for ~ (p ∧ q) is given as under:

Que-7: p ∧ (~ q)

Sol: The truth table for statement p ∨ (~ q) is given as under:

Que-8: ~ [p ∨ (~ q)]

Sol: The truth table for ~[p ∨ (~ q)] is given as under:

Que-9: ~ (~ p ∧ ~ q)

Sol: The truth table for ~ (~p ∧ ~ q) is given as under:

Que-10: (p ∧ q) ∨ (~p ∧ q)

Sol: The truth table for (p ∧ q) ∨ (~ p ∧ q) is given as under:

Que-11: p ∧ (q ∨ r)

Sol: The truth table for p ∧ (q ∨ r) is given as under:

Que-12: (~p ∧ ~ q) ∨ (p ∧ ~ q)

Sol: The truth table for (~ p ∧ ~ q) ∨ (p ∧ ~ q) is given as under:

Que-13: (p ∨ q) ∨ (r ∧ ~ q)

Sol: The truth table for (p ∨ q) ∨ (r ∧ ~ q) is given as under:

Que-14: Let p be “Ananya is beautiful,” and let q be “Ananya is 165 centimetres tall.”
(i) Under what conditions is the statement, “Ananya is beautiful and 165 centimetres tall.” true?
(ii) Under what conditions is the statement, “Ananya is beautiful and 165 centimetres tall,” false?
(iii) Under what conditions is the statement, “Ananya is beautiful or 165 centimetres tall,” true?
(iv) Under what conditions is the statement, “Ananya is beautiful or 165 centimetres tall,” false?

Sol: Given p : Ananya is beautiful
q: Ananya is 165 centimeters tall
(i) Only if Ananya is both beautiful and 165 cm tall.
(ii) If Ananya is not beautiful and/or not 165 cm tall.
(iii) If Ananya is beautiful and/or 165 cm tall.
(iv) Only if Ananya is neither beautiful nor 165 cm tall.

–: End of Mathematical Reasoning Class 11 OP Malhotra Exe-27D ISC Maths Ch-27 Solutions. :–

Return to :- OP Malhotra ISC Class-11 S Chand Publication Maths Solutions

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