Let A 1 2 3 4 Determine a codomain B and a function f A rig

Let A = {1, 2, 3, 4}. Determine a codomain B and a function f: A rightarrow B such that the following hold (briefly justify your answers). f is onto B, but not one-to-one. f is one-to-one, but not onto B. f is both one-to-one and onto B. f is neither one-to-one nor onto B.

Solution

a) B={1}

f(x)=1 for all x in A

b)

B={1,2,3,4,5}

f(x)=x is identity map which is one one but not onto as 5 is not in image of f

c)

B=A

f(x)=x ie identity map which is both one one and onto

d)

B={1,2}

f(x)=1 for all x in A