00:01
All right, so let's go ahead and construct the truth table for this statement here.
00:04
But to do that, we have to first construct just columns p, q, and r.
00:10
And so we're going to have eight combinations that we have to worry ourselves with.
00:13
I'm just going to write this in the most orderly way, so it's an easiest way to do it.
00:17
And so just let four true, four falses for p, and then go back and forth with q.
00:22
And by doing this, excuse me, while doing this, or by doing this, what you get are all the possible combinations of t, f, and t, v, true and false values given you have two statements you're working with.
00:33
So let me go ahead and write this real quick.
00:37
Okay, so we're trying to show p if and only if r or negate q if and only if r.
00:46
So we need a negation of, well, that should be negation of p, excuse me.
00:51
So we need a negate p and we need a negate q columns.
00:54
Let's figure that out first.
00:56
Negate p is just going to be the opposite of the truth values in column p.
00:59
So just write everything opposite.
01:01
And negation q is the same thing.
01:02
Just what the q column.
01:10
Okay, now q if and only if r, or negate p if and only if r, well, an if and only if statement like this actually means two things.
01:20
What it means is p implies r and r implies p.
01:26
So figuring out what these values are, are just figuring out the statements p implies r and r implies p.
01:34
If we work down here, p implies r and r implies p.
01:42
Those values right there, well, if we're just given p implies r, r implies p values here, we can actually construct with those r, so let's go in and go through them.
01:53
So p implies r, that's true, false, true, false, and everything else is true.
02:00
R implies p, true, true, true, true, true, false, true.
02:08
So now if we want that statement that we asked above, well, i'm just going to go and extend this and maybe ignore this part down here for now.
02:16
I'm not just going to consider the and of those last two statements.
02:19
So in particular, p, and this is i want to negate p.
02:24
I should have done a negate p, i apologize.
02:25
So this is negate p and negate p.
02:27
So i have to go back in and change some of these values.
02:29
So let me just do it with negation of p instead.
02:35
So negate p.
02:36
And i'll just go in and change this.
02:38
But i just wanted to illustrate the idea here.
02:41
So here's the truth values here...