Prove that P1, P2 ⊢ C P1: (∀x)(∃y)(P(x) ⇒ (Q(y) ∧ T(x, y)∧ ∼ S(x, y)))...

Prove that P1, P2 ⊢ C
P1: (∀x)(∃y)(P(x) ⇒ (Q(y) ∧ T(x, y)∧ ∼ S(x, y)))
P2: (∃x)(∀y)(P(x) ∧ ((Q(y) ∧ R(x, y)) ⇒ S(x, y)))
C: ∼ (∀x)(∀y)((P(x) ⇒∼ T(x, y)) ∨ (Q(y) ⇒ R(x, y)))

Expert Solution

When we remove universal quantifiers

It is always true for existential quantifiers

I proved this in Hilbert style

venereology answered 5 days ago

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