And you should be able to see with further manipulations that the implication is indeed true.
Look at the group . Can you find 2 elements that show this implication is not true?
I am trying to prove, or disprove by means of a counterexample the two statements.
For a subgroup H of a group G, with elements a,b G, and aH is the coset of H containing a, defined as
I'm not sure where to start on these.