Relations and Functions

An ordered pair (a

An ordered pair (a,b) is a pair of elements where order matters. For example, (3,5) is different from (5,3). Two ordered pairs (a,b) and (x,y) are equ

For two sets A and B

For two sets A and B, the Cartesian product A × B = {(a,b) : a ∈ A, b ∈ B}. If n(A) = p and n(B) = q, then n(A × B) = pq. Example: If A = {1,2} and B

A relation R from set

A relation R from set A to set B is any subset of A × B. It describes a connection between elements of A and elements of B. For example, if A = {1,2,3

A function f from set

A function f from set A to set B is a special relation where every element in A has exactly one image in B. Written as f: A → B, where f(a) = b means

For a function f

For a function f: A → B, Domain = A (set of all input values), Codomain = B (the target set), Range = set of all actual outputs. For example, if f(x)