Let S be the set containing the number 5 Let A fS S be th

Let S be the set containing the number 5. Let A = {f:S - > S} be the set of all function S - > S. For f, g E A define f ~ g if f(5) = g(5) a.Find the equivalence class of f = {(5, a), (a, b), (b, b)} in the case S = {5,a,b}.

Solution

S=(5,a,b)

f(5) = g(5) implies f ~ g

f= {(5,a) (a,a) (a,b)}

f(5) =a hence g(5) = a

Equivalence class is

{(5,a) (a,a) (b,b) } or {(5,a) (a,b) (b,b) } or

{(5,a) (a,a) (b,a) } or {(5,a) (a,b) (b,a) }