Relations

An ordered pair (a

An ordered pair (a, b) is a pair of objects where order matters. Two ordered pairs (a, b) and (c, d) are equal if and only if a = c and b = d. Unlike

For sets A and B

For 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. Generally, A × B ≠ B × A unless

A relation R from set

A relation R from set A to set B is any subset of A × B. If (a, b) ∈ R, we say 'a is related to b' and write aRb. Domain is the set of all first eleme

Empty relation (R = ∅)

Empty relation (R = ∅), Universal relation (R = A × A), Reflexive ((a,a) ∈ R for all a ∈ A), Symmetric (if (a,b) ∈ R then (b,a) ∈ R), and Transitive (

A relation that is reflexive

A relation that is reflexive, symmetric, and transitive simultaneously. Examples include similarity of triangles, congruence modulo n, and equality of