00:01
So for this problem we want to make some truth tables for some different statements.
00:04
For a we've got p, q, and r so i went ahead and filled in all the possible combinations of p, q, and r and we just want to kind of go through and build our statement.
00:14
So the first thing we have here is not q that we could make a column for so that would just take q and make them all opposite and then we can do our statement p and not q.
00:40
So we're looking at this column here and this column here.
00:43
Remember and is only true if they're both true so the first one they're not both true, not both true, and then both true, both true, no, no, and the rest of them are no's.
00:57
So that's the first half of our statement here.
01:03
We can look at the last half r or p.
01:06
Remember this is true if any of them are true so r and p is going to be this first column and the third column so that's true, true, true, true, true, false, true, false, and then we want to put it all together.
01:36
So we've got p and not q implies r or p and remember this is just saying if this thing is true then this thing is true.
01:52
So i want to look at places where if the first thing is false we don't really care it ends up being true.
02:03
So that's these first two rows here when the first one is true the second one is true so both of those are true as well and then the rest of them the first one is false so all of these end up being true here because the only way to make this false is for the first one to be true but the second one to be false.
02:27
So that's your truth table for the first one.
02:30
For the second one we've just got p and q and so i went ahead and filled that part in...