SOLUTION: Suppose Set B contains 61 elements and the total number elements in either Set A or Set B is 112. If the Sets A and B have 38 elements in common, how many elements are contained in

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Question 1047234: Suppose Set B contains 61 elements and the total number elements in either Set A or Set B is 112. If the Sets A and B have 38 elements in common, how many elements are contained in set A?
Found 3 solutions by stanbon, ikleyn, Theo:
Answer by stanbon(75887) About Me  (Show Source):
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Suppose Set B contains 61 elements and the total number elements in either Set A or Set B is 112. If the Sets A and B have 38 elements in common, how many elements are contained in set A?
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A + B - (A and B) = (A or B)
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A + 61 - 38 = 112
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A = 150-61
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A = 89 elements
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Cheers,
Stan H.
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Answer by ikleyn(52803) About Me  (Show Source):
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
set B contains 61 elements.
total number of elements in set A or set B is 112.
sets A and B have 38 element in common.

the formula is number of elements in set (A or B) is equal to the numbers of elements in set A plus the number of elements in set B minus the elements that are in both set A and set B.

the formula assumes that the elements in set A include the elements that are also in set B, and it assumes that the elements in set B include the elements that are also in set A.

because of this, the elements in set A and B are double counted, once as part of set A and again as part of set B.

the subtraction of the number of elements in both set A and B eliminates the double counting.

you get:

112 = 61 + A - 38

A represents the number of elements in set A

solve for A to get A = 112 - 61 + 38 = 89

there are 61 elements in set A and 89 elements in set B.

each set is assumed to contain elements that are in both.

take out the elements in set A that are also in set B.
take out the elements in set B that are also in set A.

you get the number of elements in set A only are 61 - 38 = 23.
you get the number of elements in set B only are 89 - 38 = 51.

now count the number of elements that are in both set A and B separately.

you get 23 in A and 51 in B and 38 in both for a total of 112.