# Question about intersection/union of a set and its complement

I was answering this multiple choice question from this website examtimequiz.com/maths-mcq-on-sets:

If $$A$$ is any set, then

1. $$A \cup A' = U$$
2. None of these
3. $$A \cap A' = U$$
4. $$A \cup A' = \emptyset$$

And is the empty (null) set finite or infinite?

• What is $\, A'$? What is $\, U$? For your other question, the empty set is a finite set since it has no elements. Oct 18, 2014 at 12:29
• actually I don't know what the question really mean I took it from this website examtimequiz.com/maths-mcq-on-sets
– M.A
Oct 18, 2014 at 12:37
• but I think it means that the intersection of set A and A-prime = the universal set ... but I'm not really sure =)
– M.A
Oct 18, 2014 at 12:40
• Oh ok. For me, it is impossible to know how to answer this question without knowing what $\, A'$ and $U$ are, and they could mean anything. I checked out the website you gave and it didn't help me figure out what they mean. Hopefully someone else can help you. Oct 18, 2014 at 12:41
• That site is garbage! Whoever wrote that quiz is poor at (a) English, (b) Maths, (c) Choosing HTML characters, (d) All of the above. Answer d. Apr 6, 2015 at 0:25

I believe there is a mistake. We can define $A'$ as $U \setminus A$. Also $A \subseteq U$.
Therefore $A \cup (U \setminus A) = U$ (which would be quite simple for show).
I am assuming that $A'$ = the complement of set $A$, and that $U$ = the universal set. The red part is the set $A$, and $A'$ is everything in the white. The set $U$ is everything, so the red part + the white part. That makes $A \cup A' = U$. So there was a mistake in the question and your answer is correct. 