Sets in math

Let A = {{2,3},4,{{5},6,7}}
What is true?
{2,3} is a subset of A
or
{{2,3}} is a subset of A
And is
{{5},6,7} a member of A?
Please justify your answer, this is really confusing me
Answer #1
I’m sure you have a book that explains this.
Answer #2
TheClassic replied: I'm sure you have a book that explains this.
Not really helpful..
Answer #3
No idea what it really means, but to me it looks like the first one is true, simply because the {2,3} is in the original, and {{2,3}} is not
Answer #4
Just Google “Set Notation” and learn about it
eg.
http://www.purplemath.com/modules/setnotn.htm
Answer #5
What’s odd here is that A is a mixed set of subsets and objects.
1) Is {2,3} or is {{2,3}} a subset of A?
Since {2,3} is a member of A, the subset of A containing {2,3} must be {{2,3}}
The subset {2,3} only has the members 2 and 3, neither of which are members of A.
I could also say that the set:
B = {{2,3},4} is a subset of A.
2) Is {{5},6,7} a member of A?
Yes, it is because that exact set is listed in the set A.
The format of sets and subsets is weird when you allow sets of mixed subsets and simple items but you just need to remember that each item (including those wrapped in {}) are members of the set and member format must be maintained.
Answer #6
As a first step, you have to identify the members of this set. That’s just all things that are seperated by comma but that are not inside curly braces themselves (just ignore the outermost curly braces}. Thus:

• {2, 3} (Yes, this is a set by itself, but the entire set {2, 3} is a member of A
• 4
• {{5}, 6, 7}

These are all the members of A.
{2,3} is a subset of A
Remember the definition of a subset: All members of the (possible subset) must also be a member of A.

Again, you have to identify the members of B as a first step:

• 2
• 3

Are both of these listed by themselves in the first list denoting the members of A? No, they’re not!
{{5},6,7} a member of A?
Can’t say much more regarding this than Belderan. Now you’re being asked whether this set is a member of A, i.e. does it exist in the first list? Yes, it does.
Answer #7
Good, verbose explanation, GS Thanks for clearing up my lazy one.