Question 1 of 20
Determine the truth value for the statement when $p$ is true, $q$ is false, and $r$ is false.
\[
q \rightarrow(p \wedge r)
\]
Answer
Final Answer: The truth value for the statement when $p$ is true, $q$ is false, and $r$ is false is \(\boxed{True}\).
Step 1 ：The given statement is a logical implication, which is true except for the case where the antecedent (the part before the arrow) is true and the consequent (the part after the arrow) is false.
Step 2 ：In this case, $q$ is false and $(p \land r)$ is also false (since $r$ is false).
Step 3 ：Therefore, the statement is true because a false antecedent makes the implication true.
Step 4 ：Final Answer: The truth value for the statement when $p$ is true, $q$ is false, and $r$ is false is \(\boxed{True}\).
