For two statements p and q , the logical statement (p ⇒ q) ∧ (q ⇒ p) is equivalent to

Correct answer: C. p p q p → q p q → p (p → q) ∧ (q → p) T T T F F F T F F F T F F T T T T T F F T T T T Clearly, (p → q) ∧ (q → p) is equivalent to p

NTA Abhyas 2020

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

NTA Abhyas 2020 · Mathematics · Mathematical Reasoning

For two statements p and q , the logical statement (p ⇒ q) ∧ (q ⇒...

For two statements

p and q

, the logical statement \left(p ⇒ q\right)

∧ \left(q ⇒ p\right)

is equivalent to

Options

A $p$
B $q$
C $p$
D $q$

Correct answer

C. $p$

Step-by-step solution

$p$	$q$	$p \to q$	$p$	$q \to p$	\left(p \to q\right) $∧ \left(q \to p\right)$
T	T	T	F	F	F
T	F	F	F	T	F
F	T	T	T	T	T
F	F	T	T	T	T

Clearly,

\left(p \to q\right) ∧ \left(q \to p\right) is equivalent

to p

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