Q BgQuestion:

Pupil
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posted by  Rescue me on 6/10/2008 10:48:32 AM  |  status: Live  

is my answer correct?

Course Textbook Chapter Problem
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Question Details:
+ is a symbol for exclusive or
Show that (A+B)+C on venn diagram
 
show that (A+B) +B on venn diagram.
 
i drew them and concluded this. is it correct??
 

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Oracle
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posted by gomorycut on 6/10/2008 6:17:44 PM  |  status: Live
Asker's Rating: Lifesaver   
Rescue me's comment:
"Thanks! By any chance do you happen to know a website with more XOR examples?"
Response Details:

The first one seems fine.

The second one, however, is not correct. Firstly, notice that (A+B)+B does not depend on C, so draw it out without C to avoid further confusion.
 
The area of A+B (with "+" being XOR) in the diagram below is regions 1 and 3
 
 
Now XOR is just like "their union minus their intersection." So the result is just the set A (regions 1 and 2)
 
In fact, XOR is associative.... (A+B)+C = A+(B+C)
and also B+B = empty set, and so
(A+B) + B = A+(B+B) = A + empty set = A.
 
 

Feel free to send me a private message with any followup questions if there is something you want clarified or re-explained.

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