Question Bank No: 1

1. If p is any statement, t is tautology and c is a contradiction, then which of the following is not correct?

 a)P ∨ (~p) = c
 b)p ∨ t = t
 c)p ∧ t = p
 d)p ∧ c = c

2. Which of the following pairs of statements are logically equivalent?

 a)~ (~ p) = p
 b)p ∨ (p ∧ q) and q
 c)~ (p ∧ q) and (~ p) ∨ (~ q)
 d)~ [(~ p) ∧q] and p ∨ (~ q))

3. Which of the following are not logically equivalent?

 a)~ (p → q) and (p ∧ q)
 b)~ (p ∨ q) and (~ p) ∧ (~ q)
 c)p → q and (~ p) ∧ q
 d)~ [p ∨ (~ q)] and (~ p) ∧ q

4. Each of the following statement is represented symbolically. Which one is not correct? P : It is raining; q: It is pleasent.

 a)It is raining and pleaseant p ∨ q
 b)It is not raining still it is pleasant (~ p) ∧ q
 c)It is neither raining nor pleasant (~ p) ∧ (~ q)
 d)If it rains, it will be pleasant p → q

5. Negation of each of the following conjunctions is given. Which one is not correct.

 a)Delhi is in India and London is in England. Delhi is not in India or London is not in England
 b)3+7=10and9<123+7≠10or9⊀12
 c)ram is honest or kailash is dishonest. Ram is not honest and Kailash is not dishonest
 d)19>13or12<1519⊁13or12≮15

6. Which of the following is not correct?

 a)~ (p ∧ q) = (~ p) ∨ (~ q)
 b)Truth value of p ∧ q = truth value of q ∧ p
 c)~(~ p) = p
 d)p ⇔ q ≡ (p → q) ∨ (q → p)

7. Truth value of each of the following statements is given. Which one is incorrect?

 a)Every set is an empty set False
 b)2 + 11 = 12 True
 c)0 is a real number True
 d)3 + 7 < 5 False

8. Which of the following is a statement?

 a)Please help me
 b)Hurrah ! India India has won the match
 c)Good night to all
 d)17 is a prime number

9. Which of the following is not a statement?

 a)Two plus three is seven
 b)A triangle has four sides
 c)have you ever been to Delhi?
 d)5 is an odd number

10. Which of the following is not a statement?

 a)4 is an even integer
 b)The sum of interior angles of a triangle is 1800
 c)Every square is a rhombus
 d)Do your work