Question 6: If \(U=\{1,2,3,\ldots ,20\}\) and \(A=\{1,3,5,\ldots ,19\}\), verify the following:
\((i)\) \(\;\) \(A\cup {A}’ =U \)
Solution:
\({A}’=U-A\)
\(\ \ \ \ \ \ \ \ \ \ \ =\ \)\(\{1,2,3,\ldots ,20\}\)\(\ -\ \)\(\{1,3,5,\ldots ,19\}\)
\(\ \ \ \ \ \ \ \ \ \ \ =\ \)\(\{2,4,6,\ldots,20\}\)
\(A\cup {A}’=\{1,3,5,\ldots ,19\}\)\(\cup\)\(\{2,4,6,\ldots,20\}\)
\(\ \ \ \ \ \ \ \ \ \ \ =\ \)\(\{1,2,3,\ldots ,20\}\)
\(\ \ \ \ \ \ \ \ \ \ \ =U\)