Question

3. Write the argument using propositional wffs (use statement letters shown). Then prove that the argument is valid. It is false that if Dave is Andy’s Brother, then Andy is tall. Also, If Andy is not tall, then, Chris is Andy’s cousin. Hence, If Dave is Andy’s Brother, then Chris is Andy’s cousin.(D, A, C)

Answer 1

WFFS

1. It is false that if Dave is Andy’s Brother, then Andy is tall.

~(D -> A)
D ^ ~A

2. If Andy is not tall, then, Chris is Andy’s cousin.

~A -> C

If Dave is Andy’s Brother, then Chris is Andy’s cousin.(D, A, C)

D -> C

Proof
1. ~(D -> A) [premise]
2. ~A -> C [premise]
3. ~(~D v A) [1 implication]
4. D ∧ ~A [3 DeMorgan's law]
5. D [Assume]
6. ~A [4 simplification]
7. C [2, 6 Modus Ponens]
8. D -> C [From 5 to 7 conclusion]

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