Set theory basics:
Example set:
Set of numbers less than 5 but greater than 1 = {2, 3, 4, 5}. Call the set "S".
Notation used:
{2, 3, 4, 5}
Read as: The set that contains the numbers 2, 3, 4, 5.
2 ∈ S and 6 ∉ S
Read as: 2 is an element of set S and 6 is not an element of S.
Subset: B is a subset of A if all elements of B are elements of A.
Example subset:
Notation used:
B ⊆ A
Read as: B is a subset of A.
Proper subset: B is a proper subset of A if all elements of B are elements of A and A has elements that B does not.
Example of proper subsets:
A = {1, 2, 3, 4, 5, 6}, B = {1, 2, 3}. B is a proper subset of A since every member of B is a member of A and A has members that B does not.
Notation used:
B ⊂ A
Read as: B is a proper subset of A.
Power set: The power set of any set A is the set of all possible subsets of A.
Example of power set:
S = {1, 2, 3}
Power set of S = {{∅}, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}}
Notation used:
ℙ(S)
Set Union: The union of two or more sets is the set that contains all and only members of the sets in question.
Example of set union:
A = {1, 2, 3}, B = {4, 5, 6}
The union of A and B = {1, 2, 3, 4, 5, 6}
Notation used:
A∪B = The union of A and B
Set intersection: The set of all common elements between two or more sets.
Example of set intersection:
A = {1, 2, 3}, B = {3, 4, 5}
The intersection of A and B = {3}
Notation used:
A∩B = The intersection of A and B.
