## Thinking Mathematically (6th Edition)

The provided compound statement in symbolic form is$\sim \left( p\to q \right)$. Substitute the truth values for simple statements$p,q,r$ to determine the truth value for the provided compound statement$\sim \left( p\to q \right)$. The provided compound statement is a negation of$\left( p\to q \right)$, which is a conditional statement. A conditional statement is false only when the antecedent is true and the consequent is false. In all other cases, it is true. Replace with the truth values of a simple statement, $\sim \left( \text{F}\to \text{T} \right)$. This implies the truth values can be rewritten as $\sim \left( \text{T} \right)$ or in the simplest form, it can be written as false. Therefore, it can be represented in the table form as: