Question

The negation of the logical statement $(p\to q)\to q$ is

• A. a tautology
• B. a fallacy
• C. $\sim (p\vee q)$
• D. $p\wedge q$

Answer 1

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

$(\sim p\vee q)\to q\equiv \sim (\sim p\vee q)\vee q$
$\Rightarrow$ Negation is $(\sim p\vee q)\wedge \sim q$
$\equiv (\sim p\wedge \sim q)\vee (q\wedge \sim q)$
$\equiv (\sim p\wedge \sim q)\vee f,$ where $f$ is fallacy.
$\equiv (\sim p\wedge \sim q)$
$\equiv \sim (p\vee q)$