December2015 Cs Q9

0. Consider the compound propositions given below as:
(a) p˅~(p˄q) (b) (p˄~q)˅~(p˄q) (c) (a) p˄(q˅r)
Which of the above propositions are tautologies?

  • Option : 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
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