Why is (A or C) not a premise used for D in the first problem and (A or B) a premise used for c in the second problem? I'm having trouble identifying premises in the proofs.
understanding premises
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discrete-mathematics
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0Were these pictures supposed to be of whole proofs? – 2017-01-31
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0yes but i just want to understand how you can identify the first premise by looking at the given statement if that makes sense – 2017-01-31
1 Answers
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There are bracketss missing in problem 1 . To be unambiguous it should (I assume) say :Prove that $$[((A\lor C)\to D)\land (\neg B)\land (A\lor B)]\implies D.$$ We have $[(\neg B)\land (A\lor B)]\implies A.$ So we have $A.$ And $A\implies (A\lor C).$ So we have $(A\lor C),$ which implies $D.$
$A\lor C$ is deduced from $(\neg B)\land (A\lor B).$