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27. Use rules of inference to show that if ∀x(P (x) → (Q(x) ∧ S(x))) and...

27. Use rules of inference to show that if ∀x(P (x) → (Q(x) ∧ S(x))) and ∀x(P (x) ∧ R(x)) are true, then ∀x(R(x) ∧ S(x)) is true.

29. Use rules of inference to show that if ∀x(P(x) ∨ Q(x)), ∀x(¬Q(x) ∨ S(x)), ∀x(R(x) → ¬S(x)), and ∃x¬P(x) are true, then ∃x¬R(x) is true.
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Soluton Pl*) → (.@cx, n s(»)) vs,(U) US, (2) 5. PCX) 8· @dx) , (2) , Ua, (Cio). FG Essetial genealisathien ES :ESsenta Specfi2 asons 29 Steps Premise exislentla) inslanlialtion ICing ti) Premise ん(p1%) V@cx)) .. 4. universaj instontation ucing (3) Dis junotive Sgllogtsm using C tI) and C, Premis universal Instation ucin? (6) 8. SCC) bisjunchve sylloao<im cis ng (5) and G.) Premisei univerca] instantatien sna () Modus toll ucing (0) and CIo) 12- Rex) existential genevali 3atioo caang (tl)

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