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And

The statement...

Question

The statement $(p \lor q) \land (\sim p \land \sim q)$ is

A

a tautology

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B

a contradiction

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C

a contingency

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D

logically equivalent to

x \lor (\sim x)

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Solution

The correct option is B a contradiction
$(p \lor q) \land (\sim p \land \sim q)$

We know , $\sim (p \lor q) \equiv (\sim p \land \sim q)$

$∴$ The given expression can be written as

$(p \lor q) \land (\sim (p \lor q)) \equiv x \land (\sim x)$

Conjunction of a statement and its negation is always False ,

So, it's a Contardiction

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