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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?

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Most likely it is a typo.

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

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  • $\begingroup$ Yeah, I just wanted some validation because this was a nationally applied test, and you have to do a whole thing to get a question to be reviewed and I didn't want to do it if I wasn't absolutely sure of it. Thanks! $\endgroup$ – Matheus Fernandes Sep 20 '17 at 7:14

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