Homework 12

Read: Continue with Section 3.3.

Turn in: 3.39, 3.40, 3.41, 3.48, 3.49, 3.50

• For 3.48 and 3.49, you are given a function and need to check three things: (1) does it satisfy the homomorphic property in Definition 3.46, (2) is it one-to-one, and (3) is it onto. If any one of them fails, it is not an isomorphism.
• On 3.50 you need to first come up with a function from $\mathbb{Z}$ to $2\mathbb{Z}$, and then verify the three things listed above for 3.48 and 3.49.

Extra practice: 3.42–3.45