Use rules of inference to prove that the following argument is valid. List the rule of inference used for each step  ¬p ∨ s t → ¬s p → q p ∴q ∧ ¬t

Use the first eight rules of inference to derive the conclusion of the symbolized argument below. FPT X 2 MP Dist 1 2 3 4 D V MT DN ( ) HS DS Trans Impl PREMISE (~F V X) (P v T) PREMISE FDP PREMISE ~P PREMISE { } [ 1 CD Equiv CONCLUSION T Simp Conj Add Exp Taut ACP DM CP Com AIP Assoc IP

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Discrete Math

Use symbols to write the logical form of the following arguments. If valid, iden- tify the rule of inference that guarantees its validity. Otherwise, state whether the converse or the inverse error has been made. If you study hard for your discrete math final you will get an A. Jane got an A on her discrete math final. Therefore, Jane must have studied hard.