(P → (Q v R))  –| |–  (P → Q) v (P → R) PHIL 2303 Logic. 8.5. Tautologies and Equivalences. Practice Exercise Question B2. I'm struggling on how to solve this by means of a method of subproofs and negation rules. Use natural deduction for this. This is the only question left I have on the homework. First, prove: P → (Q v R)  |–  (P → Q) v (P → R) And then prove the other side: (P → Q) v (P → R)  |–  (P → (Q v R))

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(P → (Q v R))  –| |–  (P → Q) v (P → R)

PHIL 2303 Logic. 8.5. Tautologies and Equivalences. Practice Exercise Question B2.

I'm struggling on how to solve this by means of a method of subproofs and negation rules. Use natural deduction for this. This is the only question left I have on the homework.

First, prove:

  • P → (Q v R)  |–  (P → Q) v (P → R)

And then prove the other side:

  • (P → Q) v (P → R)  |–  (P → (Q v R))
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