Question 1 - GATE — Computer Science and Information Technology (CS) — Shift 1 — 2017 | OneNoughtOne | OneNoughtOne

GATE — Computer Science and Information Technology (CS) — Shift 1 — 2017

Question 1 of 65

Question 1

Multiple ChoiceEngineering MathematicsMathematical Logic

+1 points-0.33 points

The statement (¬ p) ⇒ (¬ q) is logically equivalent to which of the statements below?

p ⇒ q
q ⇒ p
(¬q) ∨ p
(¬p) ∨ q

Correct Answer:

I only

II and IV only

II only

II and III only

II and III are equivalent to the given statement. Applying A→B≡¬A∨B to (¬p)→(¬q) gives p∨¬q, which is exactly III after exchanging the order of the disjunction.

The contrapositive of (¬p)→(¬q) is q→p, giving II. Statements I and IV instead express p→q, which is generally different. For example p=false, q=true distinguishes the two directions.

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