# If a and B Are Two Sets Such that N ( a ) = 20 , N ( B ) = 25 \Text{ and } N ( a ∪ B ) = 40 , Then Write N ( a ∩ B ) - Mathematics

If A and B are two sets such that $n \left( A \right) = 20, n \left( B \right) = 25$\text{ and } $n \left( A \cup B \right) = 40$, then write $n \left( A \cap B \right)$

#### Solution

We have:

$n\left( A \right) = 20, n\left( B \right) = 25 \text{ and } n\left( A \cup B \right) = 40$

We know:

$n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right)$
$\Rightarrow n\left( A \cap B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cup B \right)$

= 20 + 25

$-$ 40
= 5

Concept: Subsets
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 1 Sets
Exercise 1.9 | Q 10 | Page 49