\b[True.] Suppose $A\cup B=U\sqcup V$ were a separation into nonempty relatively <open sets>. Intersecting with $A$ gives a separation unless all of the <connected> set $A$ lies on one side; similarly all of $B$ lies on one side. A point of $A\cap B$ forces both to lie on the same side. The other side would then be empty, a contradiction. Hence $A\cup B$ is <connected>.

Solution

Past exam of the options I course of the University of Oxford / 2006 / E / E2 / i / Solution

 Solution (source code)