00:01
Okay, so we want to show that a set minus v is equal to a intersected with the b's complement.
00:07
So let x be in a set minus b.
00:14
Well, what does this mean? this means that x is in a and x is not in b.
00:25
Now, by definition of complements, you have x is in a and x is in b.
00:31
Complement, then by definition of intersection, x is in a intersective with b bar.
00:38
So then you have your first result that x minus b is a subset of a intersective with the bar.
00:47
Now we want to prove the reverse direction.
00:50
So let x be in a intersect with b bar.
00:58
First thing that we'll do, x is in a and x is in a.
01:06
In b bar using definition of complements, x is in a and x is not in b.
01:18
So this means that's it.
01:23
By definition, x is in a set minus b.
01:28
So you have a in the second with b.
01:32
The subset of a set minus b.
01:35
So you go from this step to this step, because it's just a definition.
01:38
Just by the way.
01:40
So then this is your left condition and this is your right condition...