Venn Diagrams: concise statement of (AnB') U (BnA') ?

[Skelly4444]

If we have 2 events A and B with an overlapping region and we wish to just shade the circles without shading the intersection or the surrounding space, is there a more concise way than I have stated below? I cannot seem to find this example anywhere on the Internet.

(AnB') U (BnA')

I tried (AnB)' but this ends up shading the surround too, which I don't want.

Any guidance would be most welcome.

 

[Dr.Peterson]

If we have 2 events A and B with an overlapping region and we wish to just shade the circles without shading the intersection or the surrounding space, is there a more concise way than I have stated below? I cannot seem to find this example anywhere on the Internet.

(AnB') U (BnA')

Yes, that is correct: [imath](A\cap \bar{B})\cup(\bar{A}\cap B)[/imath]. This amounts to an "exclusive or", and is sometimes called the "symmetric difference".

An alternative would be [imath]A\cup B-A\cap B[/imath].

 

[Skelly4444]

Many thanks for clarifying that, if the brackets were absent, would it change anything?

 

[Skelly4444]

I am afraid it will not open that attachment, it just errors and states page not found

 

[Dr.Peterson]

Many thanks for clarifying that, if the brackets were absent, would it change anything?

I think the parentheses are required for clarity. Have you been taught any rules for precedence? If not, don't omit parentheses!

I am afraid it will not open that attachment, it just errors and states page not found

Do you mean the link? It works for me:

Definition:Symmetric Difference - ProofWiki

proofwiki.org

 

[The Highlander]

I am afraid it will not open that attachment, it just errors and states page not found

If it's of any help, here are pics of the diagram shown on the site referenced by Dr.P. ?
(Just Right Click and choose: "Save image as...")

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