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Question: Use logical equivalnces to show that the propositions !p -> (q->r) and q -> (p v r) are logically equivalent.

I AM SO DAMN CONFUSED!

I tried to solve !p -> (q -> r) first

and I only got to !p -> (!q v r)

I cant see any other rule that would apply after i get that far! Someone with some knowledge please help!

  • math -

    You'll need the logical equivalence:
    p → q ≡ !p ∨ q

    so
    !p → (q→r)
    ≡ p ∨ (!q ∨ r)

    From here, use the commutative properties to rearrange the expression and apply the equivalence (of →) again to get the desired result.

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