If A and B are two sets such that

Question:

If $A$ and $B$ are two sets such that $n(A)=37, n(B)=26$ and $n(A \cup B)=51$, find $\mathbf{n}(\mathbf{A} \cap \mathbf{B})$

Solution:

Given:

$n(A)=37$

$n(B)=26$

$n(A \cup B)=51$

To Find: $n(A \cap B)$

We know that,

$|A \cup B|=|A|+|B|-|A \cap B|$ (where $A$ and $B$ are two finite sets)

Therefore,

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

$51=37+26-n(A \cap B)$

$n(A \cap B)=63-51=12$

Therefore,

$n(A \cap B)=12$

 

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