If E is a connected subset of M, and if A and B are disjoint open sets in M with E$\displaystyle \subset$AUB, prove that either E$\displaystyle \subset$A or E$\displaystyle \subset$ B.

since we already know E$\displaystyle \subset$AUB, and A and B are disjoint, so E must be a subset of A or B, why do we even need the connectedness condition here?