Which of the following is true?
1) p ⇒ q ≡ ~ p ⇒ ~q 2) ~ (p ⇒ ~ q) ≡ ~ p ˄ q... View Article
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The negation of the compound proposition p ˅ (~ p ˅ q) is
1) (p ˄ ~ q) ˄ ~ p 2) (p ˄ ~ q) ˅ ~ p 3) (p ˅ ~... View Article
If p: It rains today, q: I go to school, r: I shall meet any friends and s: I shall go for a movie, then which of the following is the proposition? If it does not rain or if I do not go to school, then I shall meet my friend and go to a movie,
If it does not rain or if I do not go to school, then I shall meet my friend and... View Article
Which of the following is not logically equivalent to the proposition: “A real number is either rational or irrational”?
1) If a number is neither rational nor irrational then it is not real 2) If a number is not... View Article
(p ˄ ~ q) ˄ ( ~ p ˅ q) is
1) A contradiction 2) A tautology 3) Either (a) or (b) 4) Neither (a) nor (b) Solution: (1) A contradiction... View Article
~ (p ⇒ q) ⇔ ~ p ˅ ~ q is
1) A tautology 2) A contradiction 3) Neither a tautology nor a contradiction 4) Cannot come to any conclusion Solution:... View Article
If p, q, r are simple propositions with truth values T, F, T, then the truth value of (~ p ˅ q) ˄ ~ r ⇒ p is
1) True 2) False 3) True if r is false 4) True if q is true Solution: (1) True (~... View Article
Which of the following is logically equivalent to ~ (~ (P ⇒ q)?
1) p ˄ q 2) P ˄ ~ q 3) ~p ˄ q 4) ~ p ˄ ~ q Solution:... View Article
Which of the following is a contradiction?
1) (p ˄ q) ˄ ~ (p ˅ q) 2) p ˅ (~ p ˄ q) 3) (p ⇒ q)... View Article
The conditional (p ˄ q) ⇒ p is
1) A tautology 2) A fallacy i.e., contradiction 3) Neither tautology nor fallacy 4) None of these Solution: (1) A... View Article
Negation of “Ram is in Class X or Rashmi is in Class XII” is
1) Ram is not in class X but Ram is in class XII 2) Ram is not in class X... View Article
Negation of “2 + 3 = 5 and 8 < 10” is
1) 2 + 3 ≠ 5 and < 10 2) 2 + 3 = 5 and 8 ≮ 10 3)... View Article
Which of the following is a statement
1) May you live long! 2) May God bless you! 3) The sun is a star 4) Hurrah! we have... View Article
Which of the following is a statement?
1) Open the door 2) Do your homework 3) Switch on the fan 4) Two plus two is four Solution:... View Article
Let p be the statement ‘x is an irrational number’, q be the statement ‘y is a transcendental number’ and r be the statement ‘x is rational number iff y is transcendental number’. Statement I r is equivalent to either q or p. Statement II r is equivalent to ~ (p ↔ ~ q ).
Statement I r is equivalent to either q or p Statement II r is equivalent to ~ (p ↔ ~... View Article
In boolean algebra, the unit element ‘1’
1) has two values 2) is unique 3) has atleast two values 4) None of these Solution: (2) is unique... View Article
Dual of (x + y) ∙ (x + 1) = x + x ∙ y + y is
1) (x ∙ y) + (x ∙ 0) = x ∙ (x + y) ∙ y 2) (x + y)... View Article
Let a be any element in boolean algebra B. If a + x = 1 and ax = 0, then
1) x = 1 2) x = 0 3) x = a 4) x = a’ Solution: (4) x =... View Article
The boolean expression corresponding to the combinational circuit is
1) (x1 + x2 ∙ x3‘) x2 2) [x1 ∙ (x2 + x3)] + x2 3) [x1 ∙ (x2 +... View Article
In a boolean algebra B with respect to ‘ + ‘ and ‘ ∙’, x’ denotes the negation of x ϵ B. Then,
1) x – x’ = 1 and x ∙ x’ = 1 2) x + x’ = 1 and x... View Article
