# This is Daily Work 15.

Let $$H$$ be a subgroup of $$G$$ and suppose $$a,b\in G$$ are elements of $$G$$.
Let $$H$$ be a subgroup of $$G$$, and suppose $$a\in G$$ is an element.
Which of the following sets is not guaranteed to be a subgroup of $$G$$?
Let $$H_1,H_2$$ be two distinct subgroups of a group $$G$$, and let $$a \in G$$ be an element.
Under what circumstances can we have $$aH_1 = H_2$$, that is, when can a left coset of one subgroup be equal to a different subgroup?