Translate the following argument and use the truth-table method to determine whe

Question

Translate the following argument and use the truth-table method to determine whether it is valid or invalid. If God does not exist, then everything is morally permitted. If everything is morally permitted, then people should be taught that God exists. It is not the case that people should be taught that God exists./:. Therefore, God exists. KEY: God exists: G Everything is morally permitted: M People should be taught that God exists: T Translation: 1. 2. 3./- VALID/INVALID For the following pair of formulas, use the truth-table method to determine whether the first implies the second, the second implies the first, they are logically equivalent 1ST IMPLIES SECOND/2ND IMPLIES FIRST/LOGICALLY EQUIVALENT/LOGICALLY INDEPENDENT

Explanation / Answer

Translation

1. ~G -> M => ~(~G) v M => G v M
2. M -> T => ~M v T
3. ~T
/- G

4. ~G -> T => ~(~G) V T => G v T (from 1 and 2 by law of Syllogism)

5. ~(~G) => G (from 3 and 4 by rule of Inference)

G M T 1 2 3 /- T T T T T F T T T F T F T T T F T T T F T T F F T T T T F T T T T F F F T F T F T F F F T F T F F F F F F T T F

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