Which of following statement is true

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Mathematical Reasoning

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Which of the following statement is true

A

$ \sim (p \leftrightarrow \sim q)$ is tautology

B

$ \sim (p \leftrightarrow \sim q)$ is equivalent to $p \leftrightarrow q$

C

$(\,p\, \wedge \, \sim q)$ is a fallacy

D

$(\,p\, \wedge \, \sim q)\, \wedge \,( \sim p\, \wedge \,q)$ is a tautology

Solution

$p$	$q$	$-q$	$p \to q$	$q \to p$	$p \to – q$	$ – q \to p$	$p \leftrightarrow q$	$p \leftrightarrow – q'$
$T$	$T$	$F$	$T$	$T$	$F$	$T$	$T$	$F$
$T$	$F$	$T$	$F$	$T$	$T$	$T$	$F$	$T$
$F$	$T$	$F$	$T$	$F$	$T$	$T$	$F$	$T$
$F$	$F$	$T$	$T$	$T$	$T$	$F$	$T$	$F$

Standard 11

Mathematics

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