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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Mathematical Reasoning

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

If p and q are two statements, then which of the following...

If

p

and

q

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

Options

A $p ⇒ \left(p ∨ q\right)$
B $\left(p ∨ q\right) ⇒ p$
C $p ⇒ \left(p ∧ q\right)$
D $p ⇔ \left(p ⇒ q\right)$

Correct answer

A. $p ⇒ \left(p ∨ q\right)$

Step-by-step solution

$p ⇒ \left(p ∨ q\right) ≡ p ∨ ( p ∨ q ) ≡ \left( p ∨ p\right) ∨ q$

We know, $p ∨ p$ & is always true

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

&

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