00:01
In the first part of a question, we have 10 is n is equal to order of n.
00:08
This is we have to prove.
00:09
Now, as we may write, as we may write x is less than or equals to mx for m is equals to 1.
00:25
So one can write.
00:28
So one can write n is equal to order of n which is an first part now in the next part of given question we have to first determine or we have to first define what is p what is p and then and then we have to prove that p is close under union let a be any set.
01:10
Let a be any set.
01:14
Then p is the power set of a.
01:24
Let a be any set and, sorry, and p is the power set of a.
01:31
That is the set of all, that is the set of all subset of a.
01:44
Along with the null set along with null set and the set a itself and the set a itself now example take an example we will consider the set a let set a is equal to one two three containing three elements therefore we have the power set of a is equal to 2 to the power a, that is equals to the set 5, then set 1, 2, 3, 1, 2, 1, 3, 0, 3, comma, 2, 2, 2, 2, 2, 0, 3, and 2, 2, 0, 3, and this set a itself.
02:38
Then we know that if the cardinality of set a is 1, then cardinality of power set is given as 2 to the power l...