Answer
The truth value of the provided compound statement with the provided condition is true.
Work Step by Step
The provided compound statement in symbolic form is\[\left( p\wedge r \right)\to q\].
Substitute the truth values for simple statements\[p,q,r\] to determine the truth value for the provided compound statement\[\left( p\wedge r \right)\to q\].
The provided compound statement is conditional statement whose ingredient variables are \[\left( p\wedge r \right)\] with\[q\].
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 the variables p and r are true.
Replace with the truth values of a simple statement:\[\left( \text{F}\wedge \text{F} \right)\to \text{T}\]
This implies the truth values can be rewritten as\[\text{F}\to \text{T}\], or in the simplest form, it can be written as \[\text{T}\](true).
Therefore, it can be represented in the tabular form as
