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Construct a derivation from the premise to the conclusion using &I, &E, ∨I, ∨E, ≡ I,...

Construct a derivation from the premise to the conclusion using &I, &E, ∨I, ∨E, ≡ I, ≡ E ,⊃ I, ⊃ E,∼ I, ∼ E. (Hint: There are more than 3 steps)

(a) Premise 1: W ⊃ X

     Premise 2: X ⊃ Y

     Premise 3: Y ⊃ Z

     Premise 4: W

    Conclusion: W & Z

(b)Premise 1: (A & B) ≡ C

    Premise 2: A ≡ B

   Conclusion: A ≡ C

(c)Premise 1: B ⊃ D

Premise 2: C ⊃ D

Conclusion: (B ∨ C) ⊃ D

(d) Premise 1: B ⊃ C

Conclusion: ∼ C ⊃∼ B

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