00:01
Hi, from the question given that in part a we need to give the definition using the set builder notation for the set of operation of union, intersection and difference.
00:09
So, a union b the set builder notation will be x set of all x such that x belongs to a or x belongs to b and similarly a intersection b is set of all x such that x belongs to a and x belongs to b and difference a minus b.
00:37
So, that is equal to set of all x such that x belongs to a and x does not belongs to b or b minus a will be set of all x such that x belongs to b and x does not belongs to a.
01:03
Now, let us move on to part b.
01:06
So, part b use the definition to prove that the all sets a and b that is a minus b union b minus a will be equal to a union b minus a intersection b.
01:27
Let x belongs to a minus b union b minus a.
01:34
So, according to the above definition x belongs to a minus b or x belongs to b minus a.
01:45
Similarly, by using the above definition x belongs to a and x does not belongs to b or x belongs to b and x does not belongs to a.
02:08
So, this implies x belongs to a union b and x does not belongs to a intersection b.
02:24
So, this implies x belongs to a union b minus a intersection b...