Relations and Functions

A × B = {(a, b) : a ∈ A and b ∈ B}

A × B × C = {(a, b, c) : a ∈ A, b ∈ B and c ∈ C}

n(A × B) = pq

n(A × B × C) = pqr

R ⊆ A × B

R^{-1} = {(b, a) : (a, b) ∈ R}

Number of relations from A to B = 2^(pq)

Number of relations on A = 2^(p^2)

A relation f from A to B is a function if every element of A has exactly one image in B

Number of functions from A to B = q^p

Two functions f:A→B and g:A→B are equal if f(x) = g(x) for every x in A

A function f:A→B is real-valued if B ⊆ R

A function f:A→B is a real function if both A and B are subsets of R

t(C) = (9C)/5 + 32