Section 2.2: Problem 13 Solution
Working problems is a crucial part of learning mathematics. No one can learn... merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.
James R. Munkres
Prove part (a) of the homomorphism theorem.
Homomorphism Theorem (a). Let be a homomorphism of into , and let map the set of variables into . For any term , we have , where is computed in and is computed in .
For variables, . For constants, . For functions, by induction, .