Let H = {(1), (12)(34)} in A4. a. Show that H is not normal in A4. b. Referrin...

Let H = {(1), (12)(34)} in A₄.

a. Show that H is not normal in A₄.

b. Referring to the multiplication table for A₄ in Table 5.1 on page 111, show that, although α₆H = α₇H and α₉H = α11H, it is not true that α₆α₉H = α7α11H. Explain why this proves that the left cosets of H do not form a group under coset multiplication.