Solved on Feb 06, 2024

Austin has a good haircut.

STEP 1

Assumptions
1. Jim is a barber.
2. Everyone who gets their hair cut by Jim receives a good haircut.
3. Austin's hair was cut by Jim.

STEP 2

Based on the given information, we can deduce a logical conclusion using a form of deductive reasoning known as a syllogism.

STEP 3

The first premise of the syllogism is that everyone whose hair is cut by Jim gets a good haircut.
Premise 1: If someone’s hair is cut by Jim, then they get a good haircut.\text{Premise 1: If someone's hair is cut by Jim, then they get a good haircut.}

STEP 4

The second premise of the syllogism is that Austin's hair was cut by Jim.
Premise 2: Austin’s hair was cut by Jim.\text{Premise 2: Austin's hair was cut by Jim.}

STEP 5

From these two premises, we can deduce a conclusion by applying modus ponens, which is a rule of inference that states if "P implies Q" (Premise 1) and "P is true" (Premise 2), then "Q must also be true."

STEP 6

Apply modus ponens to the given premises to reach a conclusion.
Conclusion: Therefore, Austin got a good haircut.\text{Conclusion: Therefore, Austin got a good haircut.}
Based on the premises provided, we can deduce that Austin received a good haircut from Jim.

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