Question

Find all the left cosets (1 11) in U(30)

Answer 1

All the left cosets are "{H, 7H, 13H, 19H}".

Step-by-step explanation:

We have,

H = {1, 11}

n(H) = 2 and

U(30) = {1, 7, 11, 13, 17, 19, 23 and 29}

n(U) = 8

∴ Number of cosets = $\dfrac{n(U)}{n(H)}$

$=\dfrac{8}{2} = 4$

All the left cosets are {H, 7H, 13H, 19H}.

Hence, all the left cosets are {H, 7H, 13H, 19H}.

Answer 2

Find all the left cosets (1 11) in U(30):

Explanation:

• The objective is to find all the left cosets  (1 11)  in U(30).
• The set of U(30) ={1,7,11,13, 17, 23,29}.

• Let H={111}
• No. of left cosets of H in U(30) is |U(30)|/| H | =8/4 =2.

• Find the next two cosets by choosing an element not already appearing in previous chosen sets.
• Hence, all distinct left cosets H in U(30)  are H, 7H, 13H, 29H.