21. If Ala, b, e, dj and the function f-a,b).lb, d).(c. a),(d,e). Writ

1.	21. If Ala, b, e, dj and the function f-a,b).lb, d).(c. a),(d,e). Writef(N.C.E.R.T. Exemplar Problem
Answer» IfA={a,b,c,d}A={a,b,c,d} f={(a,b),(b,d),(c,a),(d,c)}f={(a,b),(b,d),(c,a),(d,c)} we definef−1={(b,a),(d,b),(a,c),(c,d)}f−1={(b,a),(d,b),(a,c),(c,d)} (fof−1)(a)=f(f−1(a))(fof−1)(a)=f(f−1(a)) =f(c)=f(c) =a we see that (fof−1)(x)=x(fof−1)(x)=xfor all elements ofx∈{a,b,c,d}x∈{a,b,c,d}

21. If Ala, b, e, dj and the function f-a,b).lb, d).(c. a),(d,e). Writef(N.C.E.R.T. Exemplar Problem

Answer»

IfA={a,b,c,d}A={a,b,c,d}

f={(a,b),(b,d),(c,a),(d,c)}f={(a,b),(b,d),(c,a),(d,c)}

we definef−1={(b,a),(d,b),(a,c),(c,d)}f−1={(b,a),(d,b),(a,c),(c,d)}

(fof−1)(a)=f(f−1(a))(fof−1)(a)=f(f−1(a))

=f(c)=f(c)

we see that

(fof−1)(x)=x(fof−1)(x)=xfor all elements ofx∈{a,b,c,d}x∈{a,b,c,d}