When using a truth table, the statement $\sim \mathrm { p } \wedge \sim \mathrm { q }$ is equivalent to $\sim ( \mathrm { p } \vee \mathrm { q } )$ .

Question

When using a truth table, the statement $\sim \mathrm { p } \wedge \sim \mathrm { q }$ is equivalent to $\sim ( \mathrm { p } \vee \mathrm { q } )$.

Quizplus · Accepted Answer

This is an application of De Morgan's laws, which state that the negation of a conjunction is equivalent to the disjunction of the negations, and vice versa. Thus, $\sim \mathrm { p } \wedge \sim \mathrm { q }$ is indeed equivalent to $\sim ( \mathrm { p } \vee \mathrm { q } )$.

When Using a Truth Table, the Statement ∼p∧∼q\sim \mathrm { p } \wedge \sim \mathrm { q }∼p∧∼q

When Using a Truth Table, the Statement $\sim \mathrm { p } \wedge \sim \mathrm { q }$