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Let p be the statement "17 > 13," let q be the statement "13 > 9" and let r be the statement "9 > 17". What is the truth

value of (-p^ q) → r?

O False
O True

1 Answer

4 votes

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.

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