Solution
= Solution
{c}
\b[True.] Put $\alpha=\sup A$, $\beta=\sup B$ and $u=\max\{\alpha,\beta\}$. These <suprema> exist by <completeness of the real numbers>, since the <sets> are nonempty and bounded. Every <set element> of the <union> $A\cup B$ is at most $u$, so $u$ is an <upper bound>. Conversely, every <upper bound> of $A\cup B$ bounds both $A$ and $B$, and is therefore at least both <suprema>. Thus
$$
\boxed{\sup(A\cup B)=\max\{\sup A,\sup B\}.}
$$