Final answer:
The truth value of (-p ∧ q) → r is True in propositional logic, because the left side of the implication is False and a False statement implies anything, making the implication always True.
Step-by-step explanation:
The question involves evaluating the truth value of a compound statement in propositional logic. Let's analyze each component first:
- p is the statement "17 > 13", which is True.
- q is the statement "13 > 9", which is also True.
- r is the statement "9 > 17", which is False.
We are asked to find the truth value of (-p ∧ q) → r. The symbol ∧ represents logical AND, the symbol → represents logical implication, and the dash (-) represents negation.
Let's first evaluate -p ∧ q:
- -p is False since p is True.
- q is True.
Since False ∧ True is False (because AND requires both statements to be True), the left side of the implication (-p ∧ q) is False.
In logic, a False statement implies anything, so the implication False → r is always True, regardless of the truth value of r.
Therefore, the truth value of (-p ∧ q) → r is True.