Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement.
-$\sim [ \sim \mathrm { p } \vee ( \sim \mathrm { q } \wedge \mathrm { p } ) ]$

Question

Quizplus · Accepted Answer

The inner negation $\sim \mathrm{p}$ is false because $p$ is true. The negation $\sim \mathrm{q}$ is true because $q$ is false. Thus, $\sim \mathrm{q} \wedge \mathrm{p}$ is true because both $\sim \mathrm{q}$ and $p$ are true. The disjunction $\sim \mathrm{p} \vee (\sim \mathrm{q} \wedge \mathrm{p})$ is true because one of its components $(\sim \mathrm{q} \wedge \mathrm{p})$ is true. Finally, the negation of this true statement $\sim [\sim \mathrm{p} \vee (\sim \mathrm{q} \wedge \mathrm{p})]$ is false.

Let P Represent a True Statement and Let Q Represent ∼[∼p∨(∼q∧p)]\sim [ \sim \mathrm { p } \vee ( \sim \mathrm { q } \wedge \mathrm { p } ) ]∼[∼p∨(∼q∧p)]

Let P Represent a True Statement and Let Q Represent $\sim [ \sim \mathrm { p } \vee ( \sim \mathrm { q } \wedge \mathrm { p } ) ]$