Let A and B be two sets having 4 and 7 elements respectively.
Question:

Let $A$ and $B$ be two sets having 4 and 7 elements respectively. Then write the maximum number of elements that $A \cup B$ can have.

Solution:

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

$n(A \cup B)$ is maximum when $n(A \cap B)$ is minimum

so, $n(A \cap B)=0$

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

$=4+7-0$

$=11$

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