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If p and q are simple propositions, then p ⇔ ~ q is true when

1) p is true and q is true 2) Both p and q are false 3) p is false and q is true 4) None of these Solution: (3) p is false and q is... View Article

If p and q are simple propositions, then p ⇒ q is false when

1) p is true and q is true 2) p is false and q is true 3) p is true and q is false 4) Both p and q are false Solution: (3) p is true... View Article

Negation of the compound proposition: If the examination is difficult, then I shall pass if I study hard

1) The examination is difficult and I study hard and I shall pass 2) The examination is difficult and I study hard but I shall not pass 3)... View Article

Statement-1: ~ (p ↔ ~ q) is equivalent to p ↔ q. Statement-2: ~ (p ↔ ~ q) is a tautology.

Statement-2: ~ (p ↔ ~ q) is a tautology. 1) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 2)... View Article

The output of the circuit is

1) (x2 + x3) . [(x1 . x2) . x3’] 2) (x2 + x3) . [(x1 . x2) . x3’] 3) (x2 + x3’) + [(x1 . x2) . x3’] 4) (x2 . x3) + [(x1 . x2) .... View Article

An AND gate is the Boolean function defined by

1) f (x1, x2) = x1 . x2, x1, x2 ∈ {0, 1} 2) f (x1, x2) = x1 + x2, x1, x2 ∈ {0, 1} 3) f (x1, x2) = x1, x1, x2 ∈ {0, 1} 4) f (x1, x2) =... View Article

Let p be the proposition: Mathematics is interesting and let q be the proposition that Mathematics is difficult, then the symbol p ˄ q means

1) Mathematics is interesting implies that Mathematics is difficult 2) Mathematics is interesting implies and is implied by Mathematics is... View Article

For the circuits shown below, the Boolean polynomial is

1) (~ p ˅ q) ˅ (p ˅ ~ q) 2) (~ p ˄ p) ˄ (q ˄ q) 3) (~ p ˄ ~ q) ˄ (q ˄ p) 4) (~ p ˄ q) ˅ (p ˄ ~ q) Solution: (4) (~ p ˄ q) ˅... View Article

Which Venn diagram represents the truth of the statement: “All smokers are drinkers and all drinkers are smokers”””

1) 2) 3) 4) None of these Solution: 1) All smokers are drinkers and all drinkers are smokers. S ⊆ D and D ⊆ S. This means S = D.... View Article

Negation of the proposition: If we control population growth, we prosper

1) If we do not control population growth, we prosper 2) If we control population growth, we do not prosper 3) We control population but we... View Article

The negation of the statement If I become a teacher

1) I will become a teacher and I will not open a school 2) Either I will not become a teacher or I will not open a school 3) Neither I will... View Article

Ram secures 100 marks in maths, then he will get a mobile. The converse is

1) If Ram gets a mobile, then he will not secures 100 marks 2) If Ram does not get a mobile, then he will secure 100 marks 3) If Ram will... View Article

The negation of p → (~ p ˅ q) is

1) p ˅ (p ˅ ~ q) 2) p → ~ (p ˅ q) 3) p → q 4) p ˄ ~ q Solution: (4) p ˄ ~ q... View Article

If it is raining, then I will not come. Give its contrapositive

1) If I will come, then it is not raining 2) If I will not come, then it is raining 3) If I will not come, then it is not raining 4) If... View Article

The negation of (p ˅ ~ q) ˄ q is

1) (~ p ˅ q) ˄ ~ q 2) (p ˄ ~ q) ˅ q 3) (~ p ˄ q) ˅ ~ q 4) (~ p ˄ ~ q) ˄ ~ q Solution: (3) (~ p ˄ q) ˅ ~ q... View Article

Which of the following statements is a tautology?

1) (~ q ˄ p) ˄ q 2) (~ q ˄ p) ˄ (p ˄ ~ p) 3) (~ q ˄ p) ˅ (p ˅ ~ p) 4) (p ˄ q) ˄ (~ (p ˄ q)) Solution: (3) (~ q ˄ p) ˅ (p ˅ ~ p)... View Article

Which of the following is the inverse of the proposition: If a number is a prime then it is odd.

1) If a number is not a prime then it is odd 2) If a number is not a prime then it is not odd 3) If a number is not odd then it is not a... View Article

(p ˄ ~ q) ˄ (~ p ˄ q) is

1) A tautology 2) A contradiction 3) Both a tautology and a contradiction 4) Neither a tautology nor a contradiction Solution: (2) A... View Article

Which of the following is not a proposition?

1) √3 is a prime 2) √2 is irrational 3) Mathematics is interesting 4) 5 is an even integer Solution: (3) Mathematics is interesting... View Article

The dimensions of electrical conductivity are

1) [M-1L-3T3A2] 2) [M1L3T3A2] 3) [M1L3T-3A-2] 4) [M2L3T-3A2] Answer: 1) [M-1L-3T3A2] Electrical conductivity = 1/R R = V/I... View Article

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