00:01
Okay, so let's take a look at the first one.
00:04
The left -hand side of a can be written as a, intersection, the complement of b, intersection, but this guy, thanks to the morgan's laws, is the same thing as a intersection with the complement of b, union the complement of a which is exactly a intersection with the complement of b union a intersection with the complement of a but the complement of a is the empty set so this guy is just this one which is a minus b now let's take a look at b for b what do we have for b we have we can rewrite the left -hand side as a intersection b, intersection with the complement of a.
01:05
But now, thanks to the commutativity and the associativity of the intersection, this guy is the same thing as b, intersection a with its complement.
01:17
But this guy is the empty set.
01:19
So we got the empty set, because every set intersected with the empty set is going to be empty.
01:28
Now, let's take a look at c.
01:30
Well, we have the left -hand side can be rewritten as a union, intersection, a, oh, sorry, b intersection, the complement of a.
01:45
But this guy is equal to what? this guy is equal to a intersection b, union, a intersection, its complement.
01:58
But this is the empty set...