Determine whether the statements are logically equivalent.
-$\mathrm { q } \wedge \sim \mathrm { p }$ and $\sim \mathrm { p } \rightarrow \sim \mathrm { q }$
A) Yes
B) $\mathrm { No }$

Question

Quizplus · Accepted Answer

The statements are not logically equivalent. The first statement, $q \wedge \sim p$, means "q and not p" which is true only if both q is true and p is false. The second statement, $\sim p \rightarrow \sim q$, means "if not p then not q", which is true in all cases except when p is false and q is true. These conditions do not match for all possible values of p and q, making the statements not equivalent.

Determine Whether the Statements Are Logically Equivalent q∧∼p\mathrm { q } \wedge \sim \mathrm { p }q∧∼p

Determine Whether the Statements Are Logically Equivalent $\mathrm { q } \wedge \sim \mathrm { p }$