GATE DA 2026 Q24: What X entails Y means

Sentence $X$ is said to entail Sentence $Y$ if whenever $X$ is $TRUE$ , $Y$ also must hold $TRUE$ .

Which of the following statements is/are correct if $X$ entails $Y$ ?

Try it: multiple select: one or more correct options

Select all correct options. No negative marking, no partial marks.

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Answer: A, B, C (official GATE 2026 final answer key)

Concept used: Entailment means the implication $X \Rightarrow Y$ is valid, i.e. $X \wedge \neg Y$ is unsatisfiable.

First step: Rewrite $X \Rightarrow Y$ as $\neg(X \wedge \neg Y)$ ; the converse does not follow.

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key