GATE DA 2024 Q29: Which implications of two propositions are tautologies

Let $x$ and $y$ be two propositions. Which of the following statements is a tautology / are tautologies?

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, C, D (official GATE 2024 final answer key)

Concept used: An implication $P \Rightarrow Q$ can only be false when $P$ is true and $Q$ is false.

First step: Each premise fixes $x$ and $y$ ; substitute those values into the conclusion and check whether it can be false.

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key