Sets A and B have 3 and 6 elements respectively. What can be minimum number of elements in A cup B

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1.Set Theory

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Sets $A$ and $B$ have $3$ and $6$ elements respectively. What can be the minimum number of elements in $A \cup B$

A

$3$

B

$6$

C

$9$

D

$18$

Solution

(b) $n(A \cup B) = n(A) + n(B) -n(A \cap B) $ = $3 + 6 – n(A \cap B)$

Since, maximum number of elements in $A \cap B = 3$

$\therefore $ Minimum number of elements in $A \cup B = 9 – 3 = 6$.

Standard 11

Mathematics

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