Use rules of inference and laws of logical equivalence to prove the following:
(p → q) ∧ (r → s) ∧ [t → ¬(q ∨ s)] ∧ t ⇒ (¬p ∧ ¬r)
"p \u2192 q\\equiv \\neg p\\lor q"
"r \u2192 s\\equiv \\neg r\\lor s"
"t \u2192 \u21c1(q \u2228 s)\\equiv \\neg t \\lor \\neg(q \u2228 s)"
"( \\neg t \\lor \\neg(q \u2228 s))\\land t \\equiv \\neg(q \u2228 s)\\land t"
if t is true, then:
"\\neg(q \u2228 s)\\land t \\equiv \\neg(q \u2228 s) \\equiv \\neg q \\land \\neg s"
then we get Destructive Dilemma that is Tautology:
"(p \u2192 q) \u2227 (r \u2192 s) \u2227 (\\neg q \\land \\neg s) \\implies (\u00acp \u2227 \u00acr)"
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