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Discrete Mathematics Proofs for ∃ and ∀

Discussion in 'Computer Science' started by Swaraj, Oct 8, 2018.

  1. Swaraj

    Swaraj Guest

    Premise or Given - ∃x(A(x) → B(x)) ∀x (B(x) → K(x))

    To Prove - ∃x(A(x) → K(x))

    My Solution -

    1) A(z) → B(z) From premise and Existential instantiation x for z

    2) B(z) → K(z) From premise and Universal instantiation x for z

    3) A(z) → K(z) Transitivity of 1,2

    4)∃x(A(x) → K(x)) From Existential Generalization Substitute z for x

    Am I doing this right if not is there any other way to prove it ?

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