let be the given set.
What are elements present in the set , where is super set of P
It is very important to understand that the above two are different. Think about how will you "define" ?
Your definition should be precise (basically you cannot say that it contanins nothing)
Once you do that you will understand the difference betweem the above.
So now can you see the difference between
How many elements does each have?
PS: Though I am no expert on this subject but I feel has deep rooted significance - for e.g. you can question what do you mean by a set with 0 element? Maybe someone with more relevant knowledge can comment. But the two sets you mentioned are definately very different and it would be a blunder to consider they are same.
A note on why this topic is included in basic set theory.
The set contains two elements.
Both of the elements are sets. Neither a nor b is an element of .
But we use the set to define the ordered pair .