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GATE | GATE CS Mock 2018 | Question 40
  • Last Updated : 03 Jan, 2018

Which of the following compound proposition is not tautology?
(A) ((p→q)∧(q →r))→(p→r)
(B) ((p∧q)∧(q∧r))→(p∧r)
(C) ((p⊕q)∧(q⊕r))→(p⊕r)
(D) (P V Q) Λ (P V R) → P V (Q Λ R)


Answer: (C)

Explanation: (A) ((p→q)∧(q →r))→(p→r) = pq’ + qr’ + p’ + r = q’+ q + p’ + r = True
(B) ((p∧q)∧(q∧r))→(p∧r) = p’ + q’ + r’ + pr = p’ + q’ + r’ + r = True
(C) ((p⊕q)∧(q⊕r))→(p⊕r) is not a tautology as seen by the case where p and r are T and q is F, or the case where p and r are F and q is T.
(D) (P V Q) Λ (P V R) ≡ P V (Q Λ R) = (P V Q) Λ (P V R) → P V (Q Λ R) is true and its a distributive law.

Option (C) is correct.

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