The answers to exercise marked [BB] can he found in the Back of the Book.Let A = {1, 2, 3]...

The answers to exercise marked [BB] can he found in the Back of the Book.

Let A = {1, 2, 3] and define ƒ1, f2, ƒ3, f4, f5: A → A

as follows:

f1 = {(1, 1), (2, 3), (3, 2)}

f2 = {(1, 3), (2, 2), (3, 1)}

f3 = {(1, 2), (2, 1), (3, 3)}

f4 = {(1, 2), (2, 3), (3, 1)}

f5 = {(1, 3), (2, 1), (3, 2)}

(a) Show that each composite function fi, o fj is one of the given functions, or the identity, by completing a table like the following one.4 For example, if f2of3 = f4, the entry in row f2, column f3, should be f4.

(b) Find the inverses of those of the six functions in (a) that have inverses.