Let vertex sets V1 and V2 be defined by V1 1 2 3 and V2 a b

Let vertex sets V1 and V2 be defined by V1= {1, 2, 3} and V2 = {a, b, c}. Let E1 = { { 1, 2}, {2, 3} }, and let E2 = { {a, b}, {b, c} } be the edge sets corresponding to the vertex sets V1 and V2, respectively. Write as a set of ordered pairs a function f:V1V2 that is a bijection from V1 to V2.

Solution

As it is a bijection from V1 to V2 that means function f will be a one-one ONTO function, that means each element of set V1 will be associated with one and only one element of set V2 and also each element of set V2 will have a preimage in set V1. So such product will actually be such that each vertex of V1 will associate with only one vertex of set V2.

So f : V1 ---> V2 is given as :

f= {(1,a),(2,b),(3,c)}

Answer