How to solve this problem with sets?

Question

Mathematics

Now I'm taking a discrete mathematics course at Stepik.org.
I can't solve one problem with sets:

I think that all options where power is present are considered incorrect (I highlighted it in red on the screenshot), since the condition is "Always".
For example:

|A|=|B| and |C|=|D|, then |A∩C|=|B∩D|.

Power is the number of elements in a set. If A = {0,2,3} B={4,5,7} C={1,3,4} D={4,5,6}. All have power 3.
But the intersection of A and C = {3} , B and D = {4,5}. The power is different.
Here are the problems with other comparisons.

Answer 1

1. TRUE. A \cap C \in A \in B \in B \cup D (sorry for writing with TeX tags).
3. TRUE, follows from the laws of logic.
5.UPD. Still, TRUE, here it is necessary to act through x. Let $x \in A \cap C$, then $x \in A$ and $x \in C$. So, $x \in B$ and $x \in D$. Is it further clear? 3 can be solved in the same way.