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\[q\to \left( p\wedge r \right)\].
Substitute, the truth values for simple statements\[p,q,r\] to determine the truth value for the provided compound statement\[q\to \left( p\wedge r \right)\].
The provided compound statement is conditional statement whose ingredient variables are \[q\] with\[\left( p\wedge r \right)\].
A conditional statement is false only when the truth values of the antecedent is true and the consequent is false.
Here, \[\left( p\wedge r \right)\]is a conjunction statement, which is true only when both variables p and \[r\]aretrue.
Replace with the truth values of a simple statement:\[\text{T}\to \left( \text{F}\wedge \text{F} \right)\].
This implies the truth values can be rewritten as \[\text{T}\to \text{F}\] or in the simplest form it can be written as \[\text{F}\](false).
Therefore, it can be represented in the table form as:
