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

GATE — Computer Science and Information Technology (CS) — Shift 1 — 2016

Question 1 of 65

Question 1

Numerical AnswerEngineering MathematicsMathematical Logic

+1 points

Let p, q, r, s represents the following propositions.

p: x ∈ {8, 9, 10, 11, 12}

q: x is a composite number

r: x is a perfect square

s: x is a prime number

The integer x ≥ 2 which satisfies ¬ ((p ⇒ q) ∧ (¬ r ∨ ¬ s)) is __________

Correct Answer:

The integer is 11. De Morgan's law rewrites the condition as (p∧¬q)∨(r∧s): either x belongs to the displayed set and is not composite, or it is both a square and a prime.

No integer x≥2 is both a perfect square and prime. Of 8, 9, 10, 11 and 12, only 11 is not composite. Thus exactly 11 satisfies the condition.

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