Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent.
-$$p \rightarrow ( q \vee r ) , \sim p \rightarrow ( q \wedge r )$$
A) Equivalent
B) Not equivalent

Question

Quizplus · Accepted Answer

The two statements are not equivalent because $p \rightarrow ( q \vee r )$ means "if $p$ then $q$ or $r$" which allows for either $q$, $r$, or both to be true when $p$ is true. On the other hand, $\sim p \rightarrow ( q \wedge r )$ means "if not $p$ then both $q$ and $r$" which requires both $q$ and $r$ to be true when $p$ is false. These conditions do not match, making the statements not equivalent.

Use DeMorganʹs Laws or a Truth Table to Determine Whether p→(q∨r),∼p→(q∧r)p \rightarrow ( q \vee r ) , \sim p \rightarrow ( q \wedge r )p→(q∨r),∼p→(q∧r)

Use DeMorganʹs Laws or a Truth Table to Determine Whether $p \rightarrow ( q \vee r ) , \sim p \rightarrow ( q \wedge r )$