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hi welcome to online logic today we're going to be looking at seven point five the conditional proof and welcome back everyone let me start off by today we're going to be looking at seven point five the conditional proof but I have to apologize because I've had a sort of technical failure in terms of the tablet computer I've been using there something that broke down on it I've ordered a new part and I'm waiting to get it back so the meantime we're going to do this old-fashioned with pen and paper so hopefully you'll be able to see this okay I'll try the right thing as we go through but let's turn off with sort of a brief review right last time we looked at two sets of we looked on the one hand at rules of replacements and rules of implication right so the rules of replacement these are essentially deal with logically equivalent pairs that we can swap in and out of our arguments so as to build the deductive proofs it rules add implication or sort of sequence argument sequences that require the full line so we're going to do we're going to add two or things because we'll see that these is the rules of replication the rules are repetitive we covered in the first four sections of chapter seven have really allowed us really a fabulous tool for building proves but it's still incomplete in fact not everything that could be proven deductively he is proven if you only have roles or a placement rules identification so we're going to see in seven point five we're going to introduce a new thing we're going to call this the conditional proof and the conditional proof operates essentially by when you get stuck in a problem the conditional proof allows you to to begin to build a proof sequence and I guess the best way for me to explain is actually do a couple problems for you so let's start off here and let me just show you a real simple problem let's imagine for instance you have this problem if a then B and C line to here is going to be B or D then e right and then the conclusion you're looking for here is if a then e we can now if you took a look at this problem and if you want you can pause the video and sort of take your time and look at this what you'll find is that none of the rules of implication or anything you're going to help you here right because you can see it to get e you need be you could add D potentially right but in order to get B here you need a you don't have a so what can you do well you can do this thing called a conditional proof and here's what you're going to do is the first line of conditional proof is always...