Help me understand: {5} is a subset {0,2,5}

Question

The way I read it is the only element in {5} is 5 and it is a member of the set {0,2,5}. I s this true?

Answer 1

correct.

Just to antagonize you a bit more, always remember that the empty set {} is also a subset of every set.

There are 2^n subsets of a set with n members. In this case, they are

{} {0} {2} {5} {0,2} {0,5} {2,5} {0,2,5}

The set of all subsets of a set is called the power set. In this case, that would be

{{},{0},{2},{5},{0,2},{0,5},{2,5},{0,2,5}}

The members of the power set are themselves sets.