Set Theory: Is {a} a Subset of {S}?

[Panphobia]

Homework Statement

I am not sure if set theory is precalc or not but here is my question.

Find a pair set such that {a} belongs to the set and {a} is not a subset of S.

The Attempt at a Solution

So I thought that a set like this would work S = {{a}, b} because {a} belongs to the set, but in order for {a} to be a subset it has to be wrapped in more brackets so {{a}} is a subset. Am I right? If not what did I state that was wrong?

 

[Tanya Sharma]

The example you have chosen is alright ,but the reasoning doesn't looks okay .For {a} to be a subset , 'a' should be an element of the set ,not {{a}} .For example for the set {a,b} , the subsets can be {a,b},{a},{b},ø . For set {{a},b} , the subsets can be {{a},b} , {{a}} ,{b} , ø .

 

[Panphobia]

Yea I realized my explanation was wrong but ny reasoning was the same as yours