Question

Let (A7, ⊗7)=({1, 2, 3, 4, 5, 6}, ⊗7) is a group. It has two sub groups X and Y. X={1, 3, 6}, Y={2, 3, 5}. What is the order of union of subgroups?

(a) 65

(b) 5

(c) 32

(d) 18

I got this question in homework.

Origin of the question is Groups in section Groups of Discrete Mathematics

Answer 1

The correct answer is (b) 5

To elaborate: Given, (A7, ⊗7)=({1, 2, 3, 4, 5, 6}, ⊗7) and the union of two sub groups X and Y, X={1, 3, 6} Y={2, 3, 5} is X∪Y={1, 2, 3, 5, 6} i.e., 5. Here, the order of the union can not be divided by order of the group.