If p and q are two statements, then which of the following statement is a tautology

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Question: Answered & Verified by Expert

If

p

and

q

are two statements, then which of the following statement is a tautology

MathematicsMathematical ReasoningJEE Main

Options:

A $p \Rightarrow (p \lor ~ q)$
B $(p \lor q) \Rightarrow p$
C $p \Rightarrow (p \land q)$
D $p \Leftrightarrow (p \Rightarrow q)$

Solution:

2294 Upvotes Verified Answer

The correct answer is:

p \Rightarrow (p \lor ~ q)

$p \Rightarrow (p \lor ~ q) \equiv ~ p \lor (p \lor ~ q) \equiv (~ p \lor p) \lor ~ q$

We know, $~ p \lor p$ is always true

i.e. the given statement is always true, hence, a tautology

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