>>13168124I did answer the other question, the answer was four of those sets I mentioned, and listed. I had to try to assume what members you wanted numbered, since you didn't give it in your question, and left it open.
For your new question:
>How many elements out of b,c,d,e are in {b,c} given that b = {d,e}?Since you have listed b,d, and e as their own elements to be included, just as I had assumed in my last answer to your similar question, the answer here is that all of the things, b, c, d, e are in the set of {b, c}. That is four in total.
From here on, the question has been answered, and the rest is just my own rambling about possibilities.
Now that that is done, and I have given the answer, I'll tell you what I think about the set I was given, and how many elements I would normally say are in it.
{b, c} as a standalone set, I would normally say that there are two elements. And I wouldn't treat them as a singlet, but rather as a set of two. Of course, treating it as a singlet, is also possible, and correct here.
Looking at {b, c}, with the knowledge that b is {d, e}, I could list the original set as {c, d, e}. Here, I would normally say that there are 3 separate elements. But, obviously, I could alternatively include any groupings of those letters as elements. in their own right. If I did that, I could have different answers for the number of elements. But here, the simplest, and most ordinary way is to say there is three.
Different considerations of what you consider elements based on what is appropriate, creates different numbers of elements based on the total number of those. All of these are equally correct, but not all are appropriate, and the most ordinary, and normal way, is to just list the amount of separate elements and not include groupings in any way. b, in your question, is an example of a grouping.
