Question

The statement $[p\wedge (p\to q\left)\right]\to p$, is

• A. a tautology
• B. a fallacy
• C. fallacy if $q$ is false
• D. tautology if $p$ is true

Answer 1

The correct option is A a tautology

$[p\wedge (p\to q\left)\right]\to p=[p\wedge (\neg p\vee q\left)\right]\to p=\left[\right(p\wedge \neg p)\vee (p\wedge q\left)\right]\to p=(p\wedge q)\to p=\neg (p\wedge q)\vee p=(\neg p\vee \neg q)\vee p=(\neg p\vee p)\vee \neg q=\text{TRUE}\vee \neg q=\text{TRUE}$
Hence, given statement is tautology