Question

Which of the following proposition is a contradiction?

• A. $(\sim p\vee \sim q)\vee (p\vee \sim q)$
• B. $(p\to q)\vee (p\wedge \sim q)$
• C. $(\sim p\wedge q)\wedge (\sim q)$
• D. $(\sim p\wedge q)\vee (\sim q)$

Answer 1

The correct option is C $(\sim p\wedge q)\wedge (\sim q)$

Contradiction is a preposition which is always false(F).
Here $\sim \equiv negation$ and $\wedge \equiv AND$
Let $x=(\sim p\wedge q)\wedge (\sim q)$
If $p=F$ and $q=F$ then $x=F$
If $p=F$ and $q=T$ then $x=F$
If $p=T$ and $q=F$ then $x=F$
If $p=T$ and $q=T$ then $x=F$
Hence option (c) is correct