Consider the compound propositions given below as:
(a)p ∨ ~(p ∧ q)
(b)(p ∧ ~q) ∨ ~(p ∧ q)
(c)p ∧ (q ∨ r)
Which of the above propositions are tautologies?

(A) (a) and (c)
(B) (b) and (c)
(C) (a) and (b)
(D) only (a)


Answer: (D)

Explanation:

• p ∨ ~(p ∧ q) = p + (pq)` = p + p` + q` = 1 + q` = 1.This is a tautology.
• (p ∧ ~q) ∨ ~(p ∧ q) = pq` + (pq)` = pq` + p` + q` = p` + q`. This is not a tautology.
• p ∧ (q ∨ r) = pq + pr. This is not a tautology.

So, option (D) is correct

Quiz of this Question