Question

A function f:(M,∗)→(N,×) is a homomorphism if ______

(a) f(a, b) = a*b

(b) f(a, b) = a/b

(c) f(a, b) = f(a)+f(b)

(d) f(a, b) = f(a)*f(a)

The question was asked during an online interview.

I would like to ask this question from Group Axioms in division Groups of Discrete Mathematics

Answer 1

The correct choice is (b) f(a, b) = a/b

For explanation I would say: The function f is a homomorphism since f(x∗y)= f(ac, bd)= (ac)/(bd) = (a/b)(c/d) = f(x)f(y).