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# Let a and B Be Two Sets Having 3 and 6 Elements Respectively. Write the Minimum Number of Elements that a ∪ B - Mathematics

Let A and B be two sets having 3 and 6 elements respectively. Write the minimum number of elements that $A \cup B$

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#### Solution

$\text{ We know that } n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right)$
$n\left( A \cup B \right) \text{ is minimum when } n\left( A \cap B \right) \text{ is maximum }$
$so, n\left( A \cap B \right) = 3$
$\text{ Hence }, n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right)$
$= 3 + 6 - 3$
$= 6$

Concept: Subsets
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 1 Sets
Exercise 1.9 | Q 4 | Page 49
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