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.
Found 3 solutions by mananth, jim_thompson5910, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
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Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

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.
Answer by ikleyn(52779)   (Show Source): You can put this solution on YOUR website!
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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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See the lesson
    - Counting elements in sub-sets of a given finite set
in this site.


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