Mathematics For Computer Science - Set Operations

​Set operations
The main operations that can be carried out on sets are union, intersection, difference
and Cartesian product.
■ The union of sets A and B is the set of all elements that are a member of either or
both sets. The symbol ∪ is used to show union. If A = {1, 3, 7, 9} and B = {1, 2, 4, 7}
then A ∪ B = {1, 2, 3, 4, 7, 9}.
■ The intersection of sets A and B is the set of all elements that are members of both
sets. The symbol ∩ is used to show intersection. Using the same sets for A and B
above then A ∩ B = {1, 7}.
■ The difference of sets A and B is the set of all elements that are members of A but not
members of B. The symbol \ is used to show difference. Again using the same sets as
above, A \ B = {3, 9}.
■ The Cartesian product of two sets is the set of all possible ordered pairs between the
two sets. The symbol × (the same symbol that is used for multiplication) is used to
denote a cartesian product. For example, if A = {1, 7} and B = {True, False} then
A × B = {(1, True), (1, False), (7, True), (7, False)}.