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now lets investigate what it means to negate a conditional so in this case I have this conditional P implies Q and then the question is what happens if Im going to negate that particular conditional now what Im going to do is Im going to use just a bunch of logical equivalences here Im going to get some result and then were going to see whether that result makes sense to us so the first thing that I can say is that we know that that I can take this P implies Q and weve just shown that this is logically equivalent to Im not changing the knot here at all but we know that the inside the conditional is logically equivalent to not P or Q so that was one step and now I have a disjunct of an or statement and Center than a knot in front of it and we know that one of de Morgans laws applies for a scenario like this that I can take them not and I can distribute it through but it does two things it takes the order to an and and it takes a knot in front of both of the two different sides
