Exercise 2.29 from Rotman's book An Introduction to the Theory of Groups.
(H.B.Mann) Let $G$ be a finite group, and let $S$ and $T$ be (not necessarily distinct) nonempty subsets. Prove that either $G=ST$ or $|G|\geq |S|+|T|.$
I would appreciate any help in order to solve this question.
P.S. I've deleted the previuos post with the same question, because it was confuse. I am sorry for the inconvenience this might cause you.