# Is “$\emptyset$” always “$\in$” a set or is it “$\subset$” of a set? Homework Help.

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.

• Correct; $\emptyset \subseteq A$ for every $A$. – Mauro ALLEGRANZA Nov 5 '17 at 9:55
• All you said is true – Max Nov 5 '17 at 9:55
• 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. – Ennar Nov 5 '17 at 9:58
• @samjoe It is true, did you notice that OP redefined $A$ ? – Adayah Nov 5 '17 at 9:59
• @Adayah Oh missed that. Correct its true then! – samjoe Nov 5 '17 at 10:00

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