Let H be as in Exercise 3. Use Exercise 4 to decide

QUESTION:

Problem 5E

Let H be as in Exercise 3. Use Exercise 4 to decide whether or not the following cosets of H are the same.

a. 11 + H and 17 + H

b. 21 + H and 5 + H

c. 7 + H and 23 + H

Reference:

3. Let H = {0, ±3, ±6, ±9, . . .}. Find all the left cosets of H in Z.

4. Rewrite the condition a–1b ∈ H given in property 5 of the lemma on page 145 in additive notation. Assume that the group is Abelian.

Reference:

Lemma Properties of Cosets

Let H be a subgroup of G, and let a and b belong to G. Then,