Question

If $p$ is any statement, $t$ and $c$ are a tautology and a contradiction respectively, then which of the following is NOT correct?

• A. $p\wedge t\equiv p$
• B. $p\wedge c\equiv c$
• C. $p\vee t\equiv c$
• D. $p\vee c\equiv p$

Answer 1

The correct option is C $p\vee t\equiv c$

When $p$ and $q$ both are true then

$\sim (p\to q)$ and $(\sim p\vee \sim q)$ both are false

i.e. $\sim (p\to q)\leftrightarrow (\sim p\vee \sim q)$ is truewhen p and q both are false then $\sim (p\to q)$ is false and $(\sim p\vee \sim q)$ is true

i.e. $\sim (p\to q)\leftrightarrow (\sim p\vee \sim q)$ is false

Hence $\sim (p\to q)\leftrightarrow (\sim p\vee \sim q)$ is neighter tautologynor contradiction.