Question

Function f, g, h are defined on a set X = (1, 2, 3) as f = ((1, 2), (2, 3), (3, 1)}
g = {(1,2),(2,1),(3,1)} h = ((1,1), (2,2),(3,1)} i) Find fog, gof. Are they equal? ii) Find fogoh and fohog. Define partial function

Answer 1

$fog=((1,3),(2,2),(3,2)) , gof=((1,1),(2,1),(3,2))$ . Clearly they are not equal.

$fogoh=((1,3),(2,2),(3,3)).$ $fohog=((1,3),(2,2)(3,2)).$ Partial functions are functions restricted to subsets of their domain.