Under what condition is a disjunction considered false?

A disjunction, which is often represented as the logical "or" (symbolically as ( p \lor q )), is a compound statement formed by connecting two statements (let's call them ( p ) and ( q )). The fundamental rule governing disjunctions is that they are false only when both individual statements are false.

In logical terms, the disjunction ( p \lor q ) evaluates to true in all cases except for when both ( p ) and ( q ) are false. This means that if either ( p ) or ( q ) is true, the disjunction will also be true. Therefore, the condition under which the disjunction is considered false directly results from both participating statements lacking truth.

This highlights the importance of the truth values of the individual statements in determining the truth of the disjunction as a whole. Thus, the correct answer identifies the specific scenario that leads to a disjunction being false.