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

Question

Quizplus · Accepted Answer

The statement $( \mathrm { p } \vee \sim \mathrm { q } ) \rightarrow \text { must be true. }$ is not necessarily true because the truth of $q$ does not directly determine the truth of the entire expression. The expression could still be false if $p$ is false and $q$ is true, making $\sim q$ false, and thus the antecedent $(p \vee \sim q)$ false, which does not determine the truth value of the entire conditional statement without knowing the consequent.

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

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