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June 27th, 2011, 04:51 AM   #1
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Set notations


I am told that U=union and ?=intersection
So i know that AUB' means all numbers that are in a but not in B
but why does A'UB' = the numbers in the intersection? I assumed that it would mean all numbers that are in neither A or B.
Same goes for A'?B' I though that meant all numbers that are not the intersection of A and B.
Could someone please explain (preferably in layman terms)
Thank You!
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June 27th, 2011, 05:24 AM   #2
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Re: Set notations

means the element is either outside or outside .
If you hatch the region outside with diagonal lines directed from lower left to upper right, and hatch outside from upper left to lower right, you will find the cross-hatch in the region where and overlap each other. That's by Venn Diagram.
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June 27th, 2011, 07:27 AM   #3
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Re: Set notations

Hello, sallyyy!

Quote:




[color=beige] . [/color][color=blue]No![/color]

This has a UNION.

means all numbers that are in A [color=blue]or[/color] not in B.

It would be everything except the light blue region.




Quote:
[color=beige] . [/color][color=blue]It doesn't![/color]

[color=beige] . [/color][color=blue]Wrong again[/color]

Once again, this is a UNION.

means numbers that are not in A [color=blue]or[/color] not in B.

It would be everything except the dark blue region.



Quote:

[color=beige] . [/color][color=blue]No![/color]

means numbers which are not in A [color=blue]and[/color] not in B.

It would be the white region (outside the two circles).

soroban is offline  
June 27th, 2011, 05:46 PM   #4
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Let the left circle be A and right circle be B.
A?B A ?B

A?B' A'?B'

A'?B'
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June 30th, 2011, 06:34 PM   #5
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Re: Set notations

Quote:
but why does A'UB' = the numbers in the intersection? I assumed that it would mean all numbers that are in neither A or B.
You are confusing with . These are not the same thing. The entire colored area is , so the compliment of that is the area outside it, i.e. "neither." Think about how this is different from .
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