Let Aabcd Bklmn and Cxyzt Give an example of a function if s

Let A={a,b,c,d}, B={k,l,m,n}, and C={x,y,z,t}. Give an example of a function (if such a function does not exist, explain why):

a) f: AB that is both injective and surjective

b) f: AB that is neither injective nor surjective

c) f: BC that is injective, but not surjective

d) f: CA that is surjective, but not injective

e) f: CA that is invertible

A mapping f: AB is called an injective function if distinct elements of A have distinct images in B

A mapping f: AB is called an surjective function if every element of B occurs as the f-image of at least one element of A.

A mapping f: AB is invertible only if f: AB is both injective and surjective.

Given that A={a,b,c,d}, B={k,l,m,n}, and C={x,y,z,t}

a) f: AB that is both injective and surjective

Injective and Surjective : f = { (a,k), (b,l),(c,m),(d,n) }

b) f: AB that is neither injective nor surjective

Not Injective , Not Surjective : f = { (a,k), (b,l),(c,m)}

d do not have image in B = not injective

n do not have image in A = not surjective

c) f: BC that is injective, but not surjective

f = { (k,x), (l,y),(m,z) }

d) f: CA that is surjective, but not injective

f = { (y,a), (y,b) , (z,c),(t,d) }

x do not have image in A = not injective

e) f: CA that is invertible

f should be both injective and surjective.

Hence,

f = { (x,a), (y,b) , (z,c),(t,d) }