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Given, $U=\{1,2,3,4,5,6\},A=\{1,2,3\}$. We have to find the complement of the set A.

We start by,

Since set $A=\{1,2,3\}$, so $A'=\{1,2,3\}'=\{4,5,6\}$

Is the second part where I write $A'=\{1,2,3\}'$ a valid way to write 'complement of set A' ? I say that because I am not sure if we can write $\{1,2,3\}'$ as a substitute to $U-A$. Also note that I am aware of other ways to write it.So my question is mostly just a yes-no one,but any other information you provide will be very much appreciated.

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It is valid. Not really advisable, the $'$ is visually obscured. –  André Nicolas Aug 27 '13 at 16:40
    
@Andre Nicolas,Hmm. . .I should have posted it before I got a 0 out of 6 only because of notation. –  rah4927 Aug 27 '13 at 16:41
    
I haven't seen $\{1,2,3\}'$ myself but I don't see anything wrong with it since it is equal to A' by definition. Perhaps you should use bar notation or $A^{C}$. –  Eleven-Eleven Aug 27 '13 at 16:42
    
@Christopher,that's what I told the teacher,but he refused to discuss the matter any further. –  rah4927 Aug 27 '13 at 16:44
    
There are different notations. As long as you have defined what you are using... –  Eleven-Eleven Aug 27 '13 at 16:44
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1 Answer

up vote 4 down vote accepted

Like Christopher Erst, I haven't ever seen $\{1, 2, 3\}'$ used, but since $A = \{1, 2, 3\}$, it follows that $A' = \overline A = A^C = \{1, 2, 3\}'$ is valid, though I wouldn't recommend it.

What I'd suggest is a more direct approach: $A' = \{4, 5, 6\}$ (to show directly that you know what the complement $A' = U - A$ is: writing $A'$ as the set whose members/elements belong to $A'$)?

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I agree with @amWhy here. I'd stay away from it. –  Eleven-Eleven Aug 27 '13 at 16:52
    
I don't think the teacher would be satisfied with me defining what the complement of a set is.,actually.That said,thanks for the answer. –  rah4927 Aug 27 '13 at 16:54
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What I'm suggesting is this: Given the question: If $U = \{1, 2, 3, 4, 5, 6\}, \; A = \{1, 2, 3\}$, what is the complement of $A$?: I would not recommend answering as follows: $A' = \{1, 2, 3\}'$. That's just "playing with notation", and avoids answering the question. I would write $U - A $ is the complement $(A')$ of set $A$, where $A' = \{4, 5, 6\}$. –  amWhy Aug 27 '13 at 16:57
    
@amwhy,thanks.the original question gave three sets and asked us to prove (A U B)'=A' intersection B' or something similar.So I was n't really careful about all my notation,but it's my fault anyway. –  rah4927 Aug 27 '13 at 17:02
    
@amwhy,I did not the leave the answer as {1,2,3}',because as you said ,that's just playing with notation. –  rah4927 Aug 27 '13 at 17:13
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