There are two elements $$x, y$$ in a group $$\left( {G,\, * } \right)$$ such that every elements in the group can be written as a product of some number of $$x's$$ and $$y's$$ in some order. It is known that
$$x * x = y * y = x * y * x * y = y * x * y * x = e$$
where $$e$$ is the identity element. The maximum number of elements in such a group is ______.

How many onto (or subjective) functions are there form an n-element $$(n\, \ge \,2)$$ set to a 2-element set ?

For the compositive table of a cyclic group shown below

Which one of the following choices is correct?

Consider the following Hasse diagrams.

Which all of the above represent a lattice?