Answer
The truth value of the provided compound statement with the provided condition is false
Work Step by Step
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:
