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Let A and B be two non empty sets . Let A ={0,2,4,6,...} and B ={1,3,5,7,....}. Now I have a simple doubt.Can someone tell me the difference between A+ B and A union B and also how A-B is different from A intersection B? And is A-B the same as A/B ?

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    You are asking about math notation, but you are not using the conventional symbols for set operations. The usual notation for "A union B" is $A \cup B$, though some authors will use $A + B$ (and define it) if convenient for their application/context. Correspondingly the usual notation for intersection is $A \cap B$, but occasionally an author will introduce an alternative. However it would be unlikely to take the form "A-B" because that risks confusion with $A\setminus B$, ie..all elements of $A$ not belonging to $B$. – 2017-02-11
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    See this [introduction to posting here](http://math.stackexchange.com/help/notation) with mathematical expressions. – 2017-02-11
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    I want to know in standard competitive exams involving multiple choice questions if A+B is given should we consider it as equivalent to AU B? Iam confused a lot here because they don't state anything extra about this particular notation – 2017-02-11

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  1. $A+B=\{a+b | a \in A \; \text{and} \; B \in B\}$
  2. $A \cup B=\{x | x \in A \; \text{or} \; x \in B\}$
  3. $A-B=A+(-B)=\{a+(-b) | a \in A \; \text{and} \; b \in B\}$
  4. $A \cap B=\{x | x \in A \; \text{and} \; x \in B\}$.

Hope this helps you to get your answer. If not then tell me, I'll update this answer.

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    Like hardmath said above some authors use A+B as well as AUB to convey the same meaning. But I doubt so. Coz in a question like if A is compact and B is also compact then the statement A+ B is always compact is true or false. Here what does + mean ? Is it the set of all possible sums of each element one from A and one from B or can we just say it's equivalent to A U B like hardmath said above – 2017-02-11
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    According to you A-B = A/B ? Hard math and you have a conflicting stance here . Please resolve it – 2017-02-11
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    According to your description of A+B , shouldn't A-B ={a-b| a belongs to A and b belongs to B }? In your point 1. B should be b . – 2017-02-11
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    In my humble opinion, I've provided you most widely used conventions. Also every entrance exam gives you the definitions necessary for the question paper in case they want to defer with the notations. So you need not worry. In case of your doubt about compact sets, the definition that I've given is what you want to proceed with. Yes I do agree that @hardmath and me have a conflict here regarding $A-B$. I will favour his definition in this case because what he says is $A-B=A+(-B)$. – 2017-02-11
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    Please correct your answer with A+(-B) instead of A-B . Thanks – 2017-02-11
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    @shadowkh corrected. :) – 2017-02-11