GATE CSE 2021 Set 2 Q25: Is ((P∧Q)→R)→((P∧Q)→(Q→R)) a tautology?

Choose the correct choice(s) regarding the following propositional logic assertion $S$ :

$S: ((P \wedge Q) \rightarrow R) \rightarrow ((P \wedge Q) \rightarrow (Q \rightarrow R))$

Try it: multiple select: one or more correct options

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

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Answer: B, D (official GATE 2021 final answer key)

Concept used: Rewrite implications as disjunctions; $A \rightarrow A$ is always true.

First step: Expand the consequent: $\neg(P \wedge Q) \vee \neg Q \vee R = \neg P \vee \neg Q \vee R$ , and compare it with the antecedent.

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Source: official GATE 2021 Set 2 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key