Let A and B be two sets having 3 and 6 elements respectively. Wri… - Vidyadip

Question

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

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Answer

$\text{A}\cup\text{B}=\{\text{x : x}\in\text{A or x}\in\text{B}\}$
$\text{If A}\subset\text{B then A}\cup\text{B}=\{\text{x : x}\in\text{A}\}$
$\text{n(A}\cup\text{B)}=6$
$\text{If A}\not\subset\text{B = \{x : x}\in\text{A or x}\in\text{B}\}$
$\text{n(A}\cup\text{B)}>6$
The minimum number of elements that $\text{A}\cup\text{B}$ can have is 6.

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