SOLUTION: Suppose Set A contains 66 elements and Set B contains 94 elements. If Sets A and B have 1 elements in common, what is the total number elements in either Set A or Set B.
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-> SOLUTION: Suppose Set A contains 66 elements and Set B contains 94 elements. If Sets A and B have 1 elements in common, what is the total number elements in either Set A or Set B.
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Question 1155136: Suppose Set A contains 66 elements and Set B contains 94 elements. If Sets A and B have 1 elements in common, what is the total number elements in either Set A or Set B.
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set A has 66 elements, 1 of which is also in set B (since 1 is in both). So 66-1 = 65 elements are just in set A but not in set B.
set B has 94 elements, 1 of which is also in set A. So 94-1 = 93 are in set B only (but not set A).
We have:
65 elements in set A only
93 elements in set B only
1 element in both set A and set B
Add up the values:
65+93+1 = 159
Answer: 159 values are in either set or both sets at the same time.
An alternative way to get the answer is to add up the values in sets A and B
66+94 = 160
Then we subtract off 1, which is the number of elements in both sets. We do this because we double counted this value when we add up 66 and 94. So we get 160-1 = 159.
There are 66 + 94 - 1 = 159 elements in the union. ANSWER
Every time, when you have an universal set U and two its finite subsets A and B with n(A) and n(B) elements
respectively, the number of elements in their UNION (A U B) is
n(A U B) = n(A) + n(B) - n(A intersection B),
where n(A intersection B) is the number of elements in their intersection.
The last equality DESERVES you MEMORIZE it.
It is one of the basic equalities (identities) in elementary Set theory.
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