Question 1 - GATE — Computer Science and Information Technology (CS) — Shift 2 — 2016 | OneNoughtOne | OneNoughtOne

GATE — Computer Science and Information Technology (CS) — Shift 2 — 2016

Question 1 of 65

Question 1

Numerical AnswerEngineering MathematicsMathematical Logic

+1 points

Consider the following expressions:

(i) false

(ii) Q

(iii) true

(iv) P ∨ Q

(v) ¬ Q ∨ P

The number of expressions given above that are logically implied by P ∧ (P ⇒ Q) is ________

Correct Answer:

Four expressions are implied. The premise P∧(P⇒Q) forces P to be true and, by modus ponens, Q to be true.

Under that only satisfying assignment, Q, true, P∨Q and ¬Q∨P are all true; false is not. Alternatively, replace P⇒Q by ¬P∨Q and simplify the premise to P∧Q, then evaluate the five choices.

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