Answer to Question #278557 in Discrete Mathematics for Komal

Question

For each of the following sets,

a)     S={1,2,3}, T ={a, b, c}

b)     S={a, b}, T ={1,2,3,4}

c)     S={1,2,3,4}, T ={a, b}

Determine whether

1.     There is a one-to-one function f: S→T;

2.     There is an onto function f: S→T; and

3.     If there is a bijective function f: S→T.

4.     For each (1–3) if such a function exists, explicitly give it. If no function exists give a short explanation?

Answer 1

A function f is said to be one to one or injective if every member of "S" has its own unique matching member in "T".

A function f is said to be onto or Surjective if every "T" has at least one matching "S".

a. one to one because every member of "S" has its own unique matching member in "T".

b.onto because every "T" has at least one matching "S".

c. one to one and onto because every member of "S" has its own unique matching member in "T" and also every "T" has at least one matching "S".

d. neither onto nor one to one.

e. Not a function because one to many is not allowed for a function.