If f 1 3 2 1 3 4 4 2 g 1 2 2 3 3 4 4 1 h 1 2 2 4 3 1 4 3 f

If f = {(1, 3), (2, 1), (3, 4), (4, 2)}, g ={(1, 2), (2, 3), (3, 4), (4, 1)}, h = {(1, 2), (2, 4), (3, 1). (4, 3)}. find f o g g o h h o f g o g

Solution

(a). f_og:

f(g(1)) = f(2) = 1.

f(g(2)) = f(3) = 4.

f(g(3)) = f(4) = 2.

f(g(4)) = f(1) = 3.

And therefore, f _o g = {(1, 1), (2, 4), (3, 2), (4, 3)}.

(b). g_oh:

g(h(1)) = g(2) = 3.

g(h(2)) = g(4) = 1.

g(h(3)) = g(1) = 2.

g(h(4)) = g(3) = 4.

And therefore, g _o h = {(1, 3), (2, 1), (3, 2), (4, 4)}.