SOLUTION: Use the formula for the cardinal number of the union of two sets to solve the problem: Set A contains 35 elements and set B contains 22 elements. If there are 40 elements in

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Question 1019067: Use the formula for the cardinal number of the union of two sets to solve the problem:


Set A contains 35 elements and set B contains 22 elements. If there are 40 elements in (A U B) then how many elements are in (A ∩ B)?
Answer by ikleyn(52786) About Me  (Show Source):
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Use the formula for the cardinal number of the union of two sets to solve the problem:

Set A contains 35 elements and set B contains 22 elements. If there are 40 elements in (A U B) then how many elements are in (A ∩ B)?
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The cardinal number of the union of two finite sets is

| A U B | = |A| + |B| - |A ∩ B|.

where the notation |X| is used for the number of elements of the finite set X.

According to this formula,  |A ∩ B| = |A| + |B| - | A U B | = 35 + 22 - 40 = 17.

For details see the lesson Counting elements in sub-sets of a given finite set in this site.