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

Question

Quizplus · Accepted Answer

Both statements are equivalent due to DeMorgan's laws, which state that $\sim ( \mathrm { p } \vee \mathrm { q } )$ is equivalent to $( \sim \mathrm { p } \wedge \sim \mathrm { q } )$. Therefore, both expressions imply $r$ under the same conditions.

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

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