00:01
For this question, we're asked to write a truth table for the following statement.
00:07
P implies q intersection.
00:12
So an intersection is an and, not p implies not q.
00:22
All right.
00:22
So let's go ahead and work through this.
00:25
So let's start with p and q.
00:29
So remember, we could have true, true, true, false, false true, and false.
00:39
False.
00:44
All right.
00:45
And then we're going to build up to this.
00:46
We're going to build up to this.
00:47
All right.
00:48
So next we need is we need this p implies q.
00:52
So let's come up with our p implies q.
00:59
So this is an if then statement.
01:01
The only time an if then statement is false is if the condition is met, but the conclusion is not.
01:07
Right.
01:07
So it means this is true.
01:10
If the condition is true, but the if the condition is true, but the conclusion is false, this is when it's false.
01:16
So only when true implies false is a conditional false.
01:20
False implies true.
01:22
False implies false.
01:23
This is true.
01:24
Just think of any if then statement.
01:27
You know, if you do this, then i'll give you a million dollars.
01:30
The only time you lie is if you actually do it, the only time that statement is a lie is when you do what was required of you and then i don't give you a million dollars.
01:39
But any other time, that statement is true.
01:42
All right.
01:43
So then now what we need to do is we need to do is we need to.
01:45
To do, we need to do this not p, make it a little bit easier to do this conjunction there.
01:55
So this not p here, i'm going to go back to this p column and do the exact opposite.
02:01
So false, false, true, true.
02:08
All right.
02:08
And then now i'm going to put together this p implies q and not p...