Final answer:
The truth value of (¬p ∨ q) ∧ r, given that p is true, q is false, and r is true, is False.
Step-by-step explanation:
The truth value of the given expression (¬p ∨ q) ∧ r can be determined by substituting the given values of p, q, and r. Given that p is true, q is false, and r is true, we can evaluate each part of the expression step by step.
First, ¬p means the negation of p. Since p is true, the negation of true is false. So, ¬p is false.
Next, we consider ¬p ∨ q, which represents the logical OR of ¬p and q. In this case, ¬p is false and q is false. The logical OR operator returns true when at least one of the statements being ORed is true. Since both ¬p and q are false, ¬p ∨ q is also false.
Finally, we have (¬p ∨ q) ∧ r. Here, the logical AND operator is used, which returns true only when both statements being ANDed are true. Since ¬p ∨ q is false and r is true, the overall expression (¬p ∨ q) ∧ r evaluates to false.
Therefore, the truth value of (¬p ∨ q) ∧ r is False.