well you won't actually find three letters in an alphabet that only has two.
try this instead: prove that the subgroup generated by x2,xy and y2 is isomorphic to F3.
Let be the free group on two generators . Prove that the free group on 3 generators is a subgroup of .
Not completely sure how to go about doing this. So . Can I show that z can be written as the the product of 's and 's and their inverses?
Or is there some other method I should try?