Q69 / 150 · MHT CET 2017 · Mathematics

Which of the following statement pattern is a tautology?

A
$p \lor (q \to p)$
B
$∽ q \to ∽ p$
Correct answer
C
$(q \to p) \lor (∽ p \leftrightarrow q)$
D
$p \land ∽ p$

Solution

It can be done using truth or using rules of logic.
(i)

p \lor (q \to p) \equiv p \lor (∽ q \lor p) \equiv p \lor p \lor ∽ q

\equiv p \lor ∽ q

(ii)

∽ q \to ∽ p \equiv q \lor ∽ p

(iv)

p \land ∽ p \equiv F

So left is (iii)

p	q	$q \to p$	$∽ p$	$∽ p \leftrightarrow q$	$(q \to p) \lor (∽ p \leftrightarrow q)$
T	T	T	F	F	T
T	F	T	F	T	T
F	T	F	T	T	T
F	F	T	T	F	T

Hence, the correct answer is option: 'C'.

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