Question 1052806: in a survey of 100 families,the numbers that read the most recent issues of various magazines were found to be as follows:reader digest=28,reader digests and science today =8,science today=30, reader digest and caravan=10,caravan=42,science today and caravan=5, all the three magazines=3. how many read none of the three magazines? how many read caravan as their only magazines? how many read science today if and only if,they read caravan?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! in a survey of 100 families,the numbers that read the most recent issues of various magazines were found to be as follows:
reader digest=28, science today = 30 ; caravan = 42
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reader digests and science today =8
reader digest and caravan=10,
science today and caravan=5
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all the three magazines=3.
how many read none of the three magazines?
how many read caravan as their only magazines?
how many read science today if and only if,they read caravan?
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Sketch a Venn Diagram: a rectangle containing 3 intersecting circles.
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Work from inside to the outside::
Put 3 in the intersection of all three circles
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Put 5 -3 = 2 in the intersection of sci and caravan
Put 8-3 = 5 in the intersection of digests and science
Put 10-3 = 7 in the intersection of digest and caravan
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The remainder of readers digest has 28-5-7-3 = 13
The remainder of science = 30-2-5-3 = 20
The remainder of caravan = 40 -7-2-3 = 28
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Total number in the circles is 80
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Number of families in the rectangle but not in the circles = 20
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how many read none of the three magazines?:: 20
how many read caravan as their only magazines?:: 27
how many read science today if and only if,they read caravan?:: 10
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Cheers,
Stan H.
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