Let A and B be two sets having 4 and 7 elements respectively. The… - Vidyadip

Question

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

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Answer

$\text{A}\cup\text{B}=\{\text{x : x}\in\text{A or x}\in\text{B}\}$
$\text{If A}\subset\text{B then A}\cup\text{B = \{x : x}\in\text{B\}}$
$\text{n(A}\cup\text{B)}=7$
$\text{If A}\cap\text{B}\not=\{\}$
$\text{then n(A}\cup\text{B)}<11$
$\text{If A}\cap\text{B}=\{\}$
$\text{then n (A}\cup\text{B)}=11$
The maximum number of elements that $\text{A}\cup\text{B}$ can have is 11.

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