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 June 27th, 2011, 03:51 AM #1 Newbie   Joined: Nov 2010 Posts: 27 Thanks: 0 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!
 June 27th, 2011, 04:24 AM #2 Senior Member   Joined: Jun 2011 Posts: 298 Thanks: 0 Re: Set notations $A'\cup B'$ means the element is either outside $B$ or outside $A$. If you hatch the region outside $A$ with diagonal lines directed from lower left to upper right, and hatch outside $B$ from upper left to lower right, you will find the cross-hatch in the region where $A$ and $B$ overlap each other. That's by Venn Diagram.
June 27th, 2011, 06:27 AM   #3
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Re: Set notations

Hello, sallyyy!

Quote:
 $\text{I am told that }\cup\text{= union and }\cap\text{ = intersection.}$ $\text{So i know that }A\,\cup\,B'\text{ means all numbers that are in }A\text{ but not in }B.$[color=beige] . [/color][color=blue]No![/color]

This has a UNION.

$A\,\cup\,B'$ means all numbers that are in A [color=blue]or[/color] not in B.

It would be everything except the light blue region.

Quote:
 $\text{but why does }A'\,\cup\,B'\text{ = the numbers in the intersection?}$[color=beige] . [/color][color=blue]It doesn't![/color] $\text{I assumed that it would mean all numbers that are in neither }A\text{ nor }B.$[color=beige] . [/color][color=blue]Wrong again[/color]

Once again, this is a UNION.

$A'\,\cup\,B'$ means numbers that are not in A [color=blue]or[/color] not in B.

It would be everything except the dark blue region.

Quote:
 $\text{Same goes for }A'\,\cap\,B'$ $\text{I thought that meant all numbers that are not the intersection of }A\text{ and }B.$[color=beige] . [/color][color=blue]No![/color]

$A'\,\cap\,B'$ means numbers which are not in A [color=blue]and[/color] not in B.

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

 June 27th, 2011, 04:46 PM #4 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 Let the left circle be A and right circle be B. A?B                                                                                                 A ?B A?B'                                                                                                  A'?B' A'?B'
June 30th, 2011, 05:34 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 $A'\cup B'$ with $(A\cup B)'$. These are not the same thing. The entire colored area is $(A\cup B)$, so the compliment of that is the area outside it, i.e. "neither." Think about how this is different from $A'\cup B'$.

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