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I know that $\emptyset$ is a subset of every set. But I am confused when I looked at that the following question from my assignment and compared it with my solution to the original solution. There you go...

Question 1. Choose the incorrect option.

$A=\{1,2,\{3,4\},5\}$

(A) $\emptyset\in A$ or (B) $\emptyset\subset A$

From what I know till now is that the correct option is (B), but...

  1. Would option (A) be correct if it would have been presented like this--> $A=\{\emptyset,1,2,\{3,4\},5\}$. ---$1$

  2. If statement $1$ was the case would $\emptyset\in A$ be correct? and also $\emptyset\subset A$? plus $\{\emptyset\}\subset A$?

Maybe, I am misunderstanding the usage of brackets as well. Kindly help me. Thank You.

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  • $\begingroup$ Correct; $\emptyset \subseteq A$ for every $A$. $\endgroup$ – Mauro ALLEGRANZA Nov 5 '17 at 9:55
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    $\begingroup$ All you said is true $\endgroup$ – Max Nov 5 '17 at 9:55
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    $\begingroup$ Use $\in$ instead of $\epsilon$ to produce $\in$. Also, there is absolutely no need to separate every symbol with $ $. Just put whole expression inside dollar signs together. $\endgroup$ – Ennar Nov 5 '17 at 9:58
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    $\begingroup$ @samjoe It is true, did you notice that OP redefined $A$ ? $\endgroup$ – Adayah Nov 5 '17 at 9:59
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    $\begingroup$ @Adayah Oh missed that. Correct its true then! $\endgroup$ – samjoe Nov 5 '17 at 10:00
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You are right: (B) is the correct option.

If the set were $A=\{\emptyset, 1,2,\{3,4\},5\}$, then we would have $\emptyset\in A$ and $\emptyset \subset A$ and $\{\emptyset\}\subset A$.

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  • $\begingroup$ Are you sure? Am I absolutely correct? $\endgroup$ – Saksham Sharma Nov 5 '17 at 10:00
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    $\begingroup$ Yes, I'm absolutely sure $\endgroup$ – A. Goodier Nov 5 '17 at 10:01

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