Question

# If ${\text{U}} = \left\{ {1,2,3,4,5,6,7,8,9} \right\}$ and ${\text{A}} = \left\{ {1,2,3,4} \right\}$, ${\text{B}} = \left\{ {2,4,6,8} \right\}$,${\text{C}} = \left\{ {3,4,5,6} \right\}$ then prove the following: ${\text{A’}} = \left\{ {5,6,7,8,9} \right\}$.

Given, Universal set as ${\text{U}} = \left\{ {1,2,3,4,5,6,7,8,9} \right\}$
Sets ${\text{A}} = \left\{ {1,2,3,4} \right\}$, ${\text{B}} = \left\{ {2,4,6,8} \right\}$,${\text{C}} = \left\{ {3,4,5,6} \right\}$
To prove: Set ${\text{A'}} = \left\{ {5,6,7,8,9} \right\}$
i.e., ${\text{A’}} = {\text{U}} - {\text{A}} = \left\{ {1,2,3,4,5,6,7,8,9} \right\} - \left\{ {1,2,3,4} \right\} = \left\{ {5,6,7,8,9} \right\}$
Hence proved that set ${\text{A’}} = \left\{ {5,6,7,8,9} \right\}$.