Discrete Math

Usually a set is represented in two ways, namely, (1) roster notation and (2) set builder notation.

In roster notation, all the elements of the set are listed, if possible, separated by commas and enclosed within braces. A few examples of sets in roster notation are given as follows:

Superset and proper set

For example, if A = {a, b}, B = {a, b, c} and C = {b, c, a}, then A and B are subsets of C, but A is a proper subset of C, while B is not, since B = C.

Power set

Given a set S, the set of all subsets of the set S is called the power set of S and is denoted by P(S). For example, if S = {a, b, c}, P(S) is the set of all subsets of {a, b, c}. i.e., P(S) = [ , {a}, {b}, {c}, {a, b}, {b, c}, {c, a}, {a, b, c}.]

ordered pairs

multiplication of multiple sets

Difference of two sets

symmetric difference of two sets

Identities and laws

Principle of duality