00:01
Our task is to determine whether the pair of statements are logically equivalent.
00:05
And to do that, we're going to make some truth tables.
00:08
So we have two variables.
00:09
So we'll start our truth table with p and q.
00:14
So since there's two, we'll have true, true, false, false.
00:19
And then for q, it'll rotate true false, true false.
00:23
Now from that, we're going to gradually build piece by piece until we get this whole thing.
00:32
So i'm going to start with not q.
00:36
So that's just going to flip all of the q's opposite.
00:40
So from what they were.
00:43
Next, i'm going to build this part.
00:51
Now when we have this symbol, both things need to be true in order for the entire statement to be true.
00:58
So looking at p and not q, they both need to be t.
01:03
So if they're not both t, then we're going to put false.
01:09
And now i'm going to build the knot in front of that.
01:14
So p.
01:17
All that's going to do is switch all of these opposite.
01:20
From what they were.
01:24
Okay, i'm going to erase this because we're going to probably need this whole space for this very first one.
01:33
Now i'm going to go ahead and build this part.
01:39
And that means that at least one of the two have to be a true in order for the whole thing to be true.
01:45
So going back to p and q, i'm looking for, so if you look here, we're going to have true, true, true, and then because both p and q are false on the last one, it'll be false...