Question

The statement $(p\vee q)\wedge (\sim p\wedge \sim q)$ is

• A. a contradiction
• B. logically equivalent to $x\vee (\sim x)$
• C. a tautology
• D. a contingency

Answer 1

The correct option is A a contradiction

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

We know , $\sim (p\vee q)\equiv (\sim p\wedge \sim q)$

$\therefore$ The given expression can be written as

$(p\vee q)\wedge (\sim (p\vee q\left)\right)\equiv x\wedge (\sim x)$

Conjunction of a statement and its negation is always False ,

So, it's a Contardiction