The statement p → (q →p) is equivalent to(a) p →(p→q)(b) – InterviewSolution

InterviewSolution

1.

The statement p → (q →p) is equivalent to(a) p →(p→q)(b) p→(p v q)(c) p→(p ∧ q)(d) p→(p ∧ q)

Answer»

Correct option (b) p→(p v q)

Explanation:

p→ (q→p) = ~ p v (q → p)

= ~ p v (~q v p) since p v ~ p is always true

= ~ p v p v q = p→ (p v q)

Discussion

No Comment Found

Related InterviewSolutions

State the converse and contrapositive of each of the following statements: If it is hot outside, then you feel thirsty.
State the converse and contrapositive of each of the following statements: I go to a beach whenever it is a sunny day.
State the converse and contrapositive of each of the following statements:(i) p: A positive integer is prime only if it has no divisors other than 1 and itself.(ii) q: I go to a beach whenever it is a sunny day.(iii) r: If it is hot outside, then you feel thirsty.
The sentence are statement? Justify.Sum of opposite angles of a cyclic quadrilateral is 180°.
Write the negation of the following statement:All policemen are thieves.
Are the following pairs of statements are a negation of each other: (i) The number x is not a rational number. The number x is not an irrational number. (ii) The number x is not a rational number. The number x is an irrational number.
Write the negation of the following statements: p : For every positive real number x, the number (x – 1) is also positive.
Write the negation of the following statements:(i) p: For every positive real number x, the number (x – 1) is also positive.(ii) q: For every real number x, either x > 1 or x < 1.(iii) r: There exists a number x such that 0 < x < 1.
Write the negation of the statement:"Zero is a positive number".
Which of the following statement is a conjunction ?A. Ram and Shyam are friends.B. Both Ram and Shyam are tall.C. Both Ram and Shyam are enemies.D. None of the above.