Q32 / 90 · JEE Main 2017 (02 Apr) · Mathematics

The statement $(p \to q) \to [(~ p \to q) \to q]$ is

Correct answer
A
A tautology
B
Equivalent to $~ p \to q$
C
Equivalent to $p \to ~ q$
D
A fallacy

Solution

$p$	$q$	$p \to q$	$~ p$	$~ p \to q$	$(~ p \to q) \to q$	$(p \to q) \to ((~ p \to q) \to q)$
$T$	$T$	$T$	$F$	$T$	$T$	$T$
$T$	$F$	$F$	$F$	$T$	$F$	$T$
$F$	$T$	$T$	$T$	$T$	$T$	$T$
$F$	$F$	$T$	$T$	$F$	$T$	$T$

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

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