$\text { If } p \text { is false then the statement } q \rightarrow ( \sim p \vee q ) \text { must be true. }$

Question

Quizplus · Accepted Answer

Given that $p$ is false, the statement $\sim p$ is true. In the expression $q \rightarrow (\sim p \vee q)$, regardless of the truth value of $q$, the part $(\sim p \vee q)$ will always be true because $\sim p$ is true (since $p$ is false). Therefore, the implication $q \rightarrow (\sim p \vee q)$ is always true when $p$ is false, as an implication is only false when the antecedent is true and the consequent is false, which cannot happen in this case.

If p is false then the statement q→(∼p∨q) must be true. \text { If } p \text { is false then the statement } q \rightarrow ( \sim p \vee q ) \text { must be true. } If p is false then the statement q→(∼p∨q) must be true.

$\text { If } p \text { is false then the statement } q \rightarrow ( \sim p \vee q ) \text { must be true. }$