# Thread: difference between membership and subset operators

1. ## difference between membership and subset operators

I'm having difficulty understanding the difference between $\in$ and $\subset$

A question asks "true or false? $\{1,2 \} \in \{1,2, \{ \{1,2 \} \} \}$ I thought this was true but it is false.

2. ## Re: difference between membership and subset operators

1, 2, 1, 2 is not a set, so I don't know what you're referring to. Do you mean {1, 2} and {1, 2, 1, 2}? Those are sets, and they are the same set because they contain the same elements. They would also be subsets of each other.

{1} is a subset of {1, 2}. 1 is a member of {1, 2}.

3. ## Re: difference between membership and subset operators

Sorry the braces didn't show. No that's not what I meant.

4. ## Re: difference between membership and subset operators

Originally Posted by Jskid
A question asks "true or false? $\{1,2 \} \in \{1,2, \{ \{1,2 \} \} \}$ I thought this was true but it is false.
For the set {1, 2} to be inside another set, you'd have to see {1, 2} or its equivalent inside that set.

{ {1, 2} } contains {1, 2}.
{1, 2} does not contain {1, 2}. It is {1, 2}, however.

{1, 2, {{1, 2}}} does not contain {1, 2}. It has three members. We just remove the outer braces to list them: 1, 2, and {{1, 2}}. Of these members, {{1, 2}} does indeed contain {1, 2}, but the enclosing set does not.

Think of membership as "contains" and subset as "includes" and this might help.