Consider the following two propositions: [P1: (p q)] [P2:(p q) (( p) q)] If the propositio…

Question

Consider the following two propositions:

$$P1: \sim (p \to  \sim q)$$

$$P2:(p \wedge  \sim q) \wedge (( \sim p) \vee q)$$

If the proposition $$p \to (( \sim p) \vee q)$$ is evaluated as FALSE, then :

Accepted Answer

Given $p \rightarrow(\sim p \vee q)$ is false

$\Rightarrow \sim p \vee q$ is false and $p$ is true

Now $p=$ True.

$\sim T \vee q=F$

$F \vee q=F \Rightarrow q$ is false

$P 1: \sim(T \rightarrow \sim F) \equiv \sim(T \rightarrow T) \equiv$ False.

$$
\begin{aligned}
P 2:(T \wedge \sim F) \wedge(\sim T \vee F) & \equiv(T \wedge T) \wedge(F \vee F) \\
& \equiv T \wedge F \equiv \text { False }
\end{aligned}
$$

Solutions · 1