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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. $A \cup A' = \emptyset$

I answered (1), but apparently the correct answer is (3). Why?

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

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  • $\begingroup$ What is $\, A'$? What is $\, U$? For your other question, the empty set is a finite set since it has no elements. $\endgroup$
    – layman
    Oct 18, 2014 at 12:29
  • $\begingroup$ actually I don't know what the question really mean I took it from this website examtimequiz.com/maths-mcq-on-sets $\endgroup$
    – M.A
    Oct 18, 2014 at 12:37
  • $\begingroup$ but I think it means that the intersection of set A and A-prime = the universal set ... but I'm not really sure =) $\endgroup$
    – M.A
    Oct 18, 2014 at 12:40
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    $\begingroup$ 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. $\endgroup$
    – layman
    Oct 18, 2014 at 12:41
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    $\begingroup$ 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. $\endgroup$
    – Martin F
    Apr 6, 2015 at 0:25

2 Answers 2

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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).

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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.

Set Theory

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