Using the basic natural deduction rules for predicate logic, prove the validity of the following sequents: (i) $\exists x (R(x) \lor S(x)) \vdash \exists x R(x) \lor \exists x S(x)$ (8) (ii) $\forall x (P(x) \to Q(x)), \exists x (C(x) \land \neg Q(x)), \forall x (C(x) \to P(x) \lor S(x)) \vdash \exists x (C(x) \land S(x))$ (9)
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(∀x)(S(x) → E(x)) To prove this, we assume the negation of the statement and derive a contradiction. Assume: (∀x)(S(x) → E(x)) Negation: (∃x)¬(S(x) → E(x)) Now, we can use the rule of existential instantiation to introduce a new constant symbol, Show more…
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