Subsets

Q1: How do I indicate that an element belongs to a particular set?
A1: Going back to the coin example, suppose you wanted to indicate that heads was an element of the subset of coin tosses $A$.
You could write: $H\epsilon A$

Q2: What is a subset?
A2: A subset is a set whose every element belongs to another set. For example, consider the set of outcomes denoting the toss of a single die:
$D=\{1, 2, 3, 4, 5, 6\}$
Then consider the set $C=\{1, 2, 3\}$
Clearly, each element of C is also an element of D. Hence, C is a subset of D:
$B\subset D$

Also, D is a subset of itself:
$D\subset D$

Q3: What is set equality?
A3: Suppose you have 2 sets, $A$ and $B$.
$A=B$ if and only if $A\subset B $ and $B\subset A$