The statement (p → q) → [(~ p → q) → q] is

The statement

\left(p \to q\right) \to \left[\left(~ p \to q\right) \to q\right]

Options

AA tautology
BEquivalent to $~ p \to q$
CEquivalent to $p \to ~ q$
DA fallacy

Correct answer

A. A tautology

Step-by-step solution

$p$	$q$	$p \to q$	$~ p$	$~ p \to q$	\left(~ p \to q\right) \to q $</td> <td>\left(p \to q\right) \to \left(\left(~ p \to q\right) \to q\right)$
$T$	$T$	$T$	$F$	$T$	$T$	$T$
$T$	$F$	$F$	$F$	$T$	$F$	$T$
$F$	$T$	$T$	$T$	$T$	$T$	$T$
$F$	$F$	$T$	$T$	$F$	$T$	$T$

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