# Question regarding the correct use of set comparison operators

I took a test the other Sunday and one of its questions provided the following sets: $A =\{1,4,2,6,8,10\}$, $B=\{1,4,6,10\}$, $C=\{6,4,1,10\}$, and $D=\{6,4,1\}$, and then asked to pick the correct option:

a) $A = D$

b) $A\subseteq B$

c) $B\not\subset D$

d) $\emptyset \subseteq D$

e) $\emptyset = D$

The correct answer, as it says in the answer sheet we got the day after the test, is $\emptyset \subseteq D$, which, I now know to be true. However, the option I picked, $B \not\subset D$ seems correct to me, since the $B \cup D \neq D$, which I, as I understand, is the only criterion that determines whether a set is or isn't a subset of another set.

Maybe they meant $B\not\subset C$, since they didn't use $C$ in any of the options?

$B \not \subset D$ is indeed a true statement. Suppose not then $B \subseteq D$, which is impossible since $|B|>|D|.$