Is the following exercise on connected subset wrong?

Question

I think there is a problem with the following exercise from Zorich, Mathematical Analysis II - Exercise 1 in Section 9.4.1:

Show that in terms of the ambient space the property of connectedness of a set can be expressed as follows: A subset $E$ of a topological space $(X,\tau)$ is connected iff there is no pair of open subsets $A,B$ that are disjoint and such that $E\cap A\neq \emptyset$, $E\cap B\neq \emptyset$, and $E\subseteq A\cup B$.

Thanks in advance!

Edit: counterexample: $X=\{a,b,c\}$, with topology generated by $\{a,b\}$ and $\{b,c\}$, with $E=\{a,c\}$.

Answer 1

Yes, it's a mistake. It should've been: "$E\cap A$ and $E\cap B$ are disjoint" instead of "$A$ and $B$ are disjoint".