3. Difference of two sets.
If A and B two sets, then we can form a new set of elements consisting of members of set A is not a member of set B. This new set of written A - B, and read "set A less set B"; or if it is written with a set-forming notation : A - B = {x | x ∈ A and x ∉ B}.
Formed a new set of elements may also be a member of set B are not members of set A, and it is written as B - A, read as "less a set A set B"; or if it is written with a set-forming notation: B-A = {x | x ∈ B and x ∉ A}.
For example:
If A = {1, 2, 3, 4, 5, 6, 7} and B = {1, 3, 5}, then A - B = {2, 4, 6, 7}
If A = {a, b, c} and B = {a, b, c, d, e, f}, then B - A = {d, e, f}
If C = {3, 5, 7} and D = {3, 5, 7}, then A-B = {} or A - B the set is empty.
4. The set of the same Set.
Two sets A and B is said to equal if and only if every member of A is a member of B as well, or vice versa, every member of B is a member of A as well.
Two sets A and B are the same written A = B, or if written with a set forming notation set : A = B = {x | x ∈ A and x ∈ B}.
For example:
If A = {2, 3, 1, 5, 4} and B = {1, 2, 3, 4, 5}, then A = B.
If A = {b, c, d} and B = {b, c, d}, then A = B.
Note that the order of the writing member is not a problem on any set (not shown differences in membership of a set).
