Could someone help with this practice problem? Thanks.

12. 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 that is a bijection from V1 to V2, satisfying the following condition: if x and y are elements in V1 such that {x,y} is in E1, then f(x) and f(y) are elements in V2 such that {f(x),f(y)} is in E2, and show that your function f satisfies this condition.

 

 

Note: you do not need to show that your function f is a bijection (though it must be, or you won’t get any credit), but you DO need to show that it satisfies the condition “if x and y are elements in V1 such that {x,y} is in E1, then f(x) and f(y) are elements in V2 such that {f(x),f(y)} is in E2.”