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Logic Theory Proof help!

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(∃x)(Fx ⋅ Hx) ⊃ ~ (x)((Fx ∨ Gx) ⊃ ~ (Hx ∨ Gx))

Apr 24th, 2015

A conditional a CP --Assume the antecedent and deduce the consequent

A universal conditional a Universal/Conditional Proof -- Assume the instantiation of the antecedent and deduce the consequent

Otherwise  a Indirect Proof – Assume the negation of the conclusion and deduce a contraction, thus proving the conclusion.

(∃x)(Fx ⋅ Hx) ⊃ ~ (x)((Fx ∨ Gx) ⊃ ~ (Hx ∨ Gx))

1.  (∃x)(Fx ⋅ Hx)                                                           Assume

2.  Fv & (Gv V Hv)                                                                    1 EI

3.  Fv                                                                                          2 Simp

4.  Gv V Hv                                                                                2 Simp

5.  (∃x)(Fx)                                                                                3 EG

6.  (∃x)(Gy V Hy)                                                                      4 EG

7.  (∃x)(Fx) & (∃x)(Gy V Hy)                                                    5, 6 Conj

8.  (∃x)[Fx & (Gx V Hx)] É [(∃x)(Fx) & (∃x)(Gy V Hy)]           1-7 CP



Apr 24th, 2015

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