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welcome back to logic 101 im william spaniel and todays topic is conditional proofs these are going to look very similar to what we covered last time proofs by contradiction in that we are going to start by assuming that something is true and see what falls out as a result of that rather than starting by just applying or rules of inference and replacement rules right off the bat so the idea behind the conditional proof is that we want to prove a conditional statement is true something like P implies Q where P and Q can be simple sentences or compound expressions doesnt matter we begin a conditional proof by assuming that the antecedent P is true and then using our replacement rules and our rules of inference we show that Q is true as well Q must follow given that we have assumed that P is true now the reason that this works is that conditional statements tell us what must follow given that the antecedent is true so were sparing ourselves a little bit of hassle by going ahead and st
