For subsets $X$ and $Y$ of $\mathbb{R}$, define: $X*Y ≡ \{ z\in ℝ \mid\text{there exist }x\in X, y\in Y\text{ such that }z = xy \}.$
Then define for $0\lt a\lt b$, $[a,b] = \{x\in\mathbb{R}\mid a\leq x\leq b\}$ and let $X=[a,b]$.
and they ask me to find $Y\subseteq \mathbb{R}$ such that $X*Y=X$.
any ideas?