Student A tries to define a function g : Q → Z by the rule g ( m n ) = m − n , for all integers m and n with n ≠ 0 . Student B claims that g is not well defined. Justify student B’s claim.

Student A tries to define a function g:Q→Z by the rule g(mn)=m−n for all integers m and n with n≠0. Student B claims that g is not well defined. Justify student B’s claim.

Given information:

Consider that a student A tries to define a function g:Q→Z by the rule g(mn)=m−n, for all integers m and n with n≠0. And the student B claims that g is not well defined.

Concept used:

A function g:A→B is said to be well defined.

If x=y then g(x)=g(y) for every x,y∈A.

Calculation:

Now clearly the given function g:Q→Z is not well defined.

Because the fraction in domain Q has one more representations as quotients of integers.

Consider,

For 24,36∈Q and clearly 24=36