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If two sets are such that n (A intersection B) = ½ (AUB) = 6. Then a total number of elements in these sets is?A.9B.12C.16D.18

Question

If two sets are such that n (A intersection B) = ½ (AUB) = 6. Then a total number of elements in these sets is?A.9B.12C.16D.18

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Solution

To find the total number of elements in the sets A and B, we can use the formula for the union of two sets:

n(AUB) = n(A) + n(B) - n(A intersection B)

Given that n(A intersection B) = 6 and n(AUB) = ½ (AUB) = 6, we can substitute these values into the formula:

6 = n(A) + n(B) - 6

Rearranging the equation, we get:

n(A) + n(B) = 12

Since the number of elements in A and B is equal to the sum of the number of elements in each set, the total number of elements in these sets is 12.

Therefore, the correct answer is B. 12.

This problem has been solved

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