15.9 If $\{a\} \subset(A \cup B) \subset\{a, b, c, d\}$, and $a \in B, A \cap B=\varnothing$, then the number of sets $A$ that satisfy the above conditions is
(A) 5.
(B) 6.
(C) 7.
(D) 8.
(2nd "Hope Cup" National Mathematics Invitational Competition, 1991)
[Solution] $\because a \in B$, and $A \cap B=\varnothing$,
$\therefore \quad a \notin A$.
Also, $\because \quad\{a\} \subset(A \cup B) \subset\{a, b, c, d\}$,
$\therefore A$ could be $\varnothing ;\{b\} ;\{c\} ;\{d\} ;\{b, c\} ;\{b, d\} ;\{c, d\} ;\{b, c, d\}$, a total of 8 possibilities.
Therefore, the answer is $(D)$.