00:01
So for this question, we're given this expression, this binary expression, p or q or p and r is the same as the truth table for which.
00:13
And so the way we're going to approach this problem is by simply we are going to find out, we're going to first lay out the truth table for what we're given, and then we're going to compare that to the truth table for each of these.
00:32
And in fact, we could actually, so we'll lay out the truth table, but after that we could actually just simply looking at, simply by just by looking at what we're given, we should be able to find out what exactly is going to be our solution.
00:58
So the truth table for this will start with p, q, and r.
01:03
So those are minimally.
01:04
That's all we need and since we have three of those right and we also have our solution here let me just take this and i can move it i can take that and i can move it over here so we have these and then since we have three of those right so we're gonna need so we'll start with us all over here right so we have to alternate true and false so we'll do that.
01:39
And we'll need to do it eight times.
01:44
So false, true, false, true, false true.
01:54
So from there, and this is just a general truth table generation, right? so then we have to now have two falses for every true.
02:03
We have two falses and then two trues.
02:06
And then finally we have all false for the top four.
02:09
And then all true for the bottom four.
02:11
And that's just simple truth, table generation.
02:14
So we can get every possible combination.
02:16
So now we start with all of them as false.
02:18
So if we have false or false, right, we're going to get false.
02:23
Or false and false, so it's going to be true.
02:27
So, sorry, it's going to be false.
02:29
And so we're false or false will give us false here.
02:33
And so we could go ahead and do the same thing.
02:35
False or false will give us false.
02:37
As long as we're getting false here, you see the, the sort of idea here is that we'll get false here, and if we get false here, then we're getting it false.
02:48
If we get true, then we're going to get true.
02:50
So for the second row here, we'll have false or false, which is false.
02:54
And on this side, we'll have false or true, or false and true, which is also false.
02:59
So once again, we'll have false.
03:02
And then next we'll have false or true, and that'll give us true on one side, on this side.
03:09
And so as long as one of these sides is true, it's going to become.
03:11
True so we don't even need to regard p and r but in case you do it it comes out to false and then for the next one we have the same case here it's going to be false and true or false or true which gives us true and then at the bottom here we'll have once again false or true that will also give us true and then we go into false or true that'll give us true and then true or true gives us true and on the other side will also come up with true and that's very last finally we have true so everything is going to be true except for the first two cases and the first two cases are when all of them are false or when only p and q are false so if p or only p and q both are false i should say so then we can look at our answer choices right and our answer choices we have p and a p or r and p or q so if we look at this let's look at the cases only to make it false, right? and when we look at the cases only to make it false, we'll have all p, q, and r, all three should be false...