Which of following is a contradiction

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Mathematical Reasoning

medium

Which of the following is a contradiction

A

$(p \wedge q) \wedge \sim (p \vee q)$

B

$p \vee (\sim p \wedge q)$

C

$(p \Rightarrow q) \Rightarrow p$

D

None of these

Solution

(a) $(p \wedge q) \wedge (\sim(p \vee q))$ is a contradiction.

$p$	$q$	$p \wedge q$	$p \vee q$	$\sim (p \vee q)$	$(p\wedge q)\ \wedge \sim(p\vee q)$
$T$	$T$	$T$	$T$	$F$	$F$
$T$	$F$	$F$	$T$	$F$	$F$
$F$	$T$	$F$	$T$	$F$	$F$
$F$	$F$	$F$	$F$	$T$	$F$

Standard 11

Mathematics

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