Archives

The proposition (p ⇒ ~ p) ˄ (~ p ⇒ p) is a

1) Tautology and contradiction 2) Neither tautology nor contradiction 3) Contradiction 4) Tautology Solution: (3) Contradiction... View Article

~ (p ˅ q) ˅ (~ p ˄ q) is logically equivalent to

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

Which of the following is true?

1) p ⇒ q ≡ ~ p ⇒ ~q 2) ~ (p ⇒ ~ q) ≡ ~ p ˄ q 3) ~ (~ p ⇒ ~ q) ≡ ~ p ˄ q 4) ~ (p ⇔ q) ≡ [ ~ (p ⇒ q) ˄ ~ (q ⇒ p)] Solution: (3) ~ (~ p... View Article

The negation of the compound proposition p ˅ (~ p ˅ q) is

1) (p ˄ ~ q) ˄ ~ p 2) (p ˄ ~ q) ˅ ~ p 3) (p ˅ ~ q) ˅ ~ p 4) None of these Solution: (1) (p ˄ ~ q) ˄ ~ 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 go to a movie, 1) ~ (p ˄ q) ⇒ (r ˄ s) 2) ~ (p ˄ ~ q) ⇒ (r ˄... 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 a rational or not an irrational, then it is not real... 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: (3) Neither a... 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 (~ p ˅ q) means F ˅ F, ~ r means F (~ p ˅ q) ˄ ~ r... 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: (4) ~ p ˄ ~ q... View Article

Which of the following is a contradiction?

1) (p ˄ q) ˄ ~ (p ˅ q) 2) p ˅ (~ p ˄ q) 3) (p ⇒ q) ⇒ p 4) None of these Solution: (1) (p ˄ q) ˄ ~ (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 tautology... 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 but Rashmi is not in class XII 3) Either Ram is not in Class X or Ram... 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) 2 + 3 ≠ 5 or 8 ≮ 10 4) None of these Solution: (3) 2 + 3 ≠ 5 or 8 ≮ 10... 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 won the match Solution: (3) The sun is a star... 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: (4) Two plus two is four Choice 1:... 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 ↔ ~ q ). 1) Statement I is correct, Statement II is correct;... View Article

M	T	W	T	F	S	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28	29	30	31