Question

Find the complement of the set given that U= {3,4,5,6,7,8,9,10,11} (use the roster method to write the set. Enter empty or 0 the empty set.) {5,7,9,10}

Answer 1

Let

`\begin{gathered} U=\mleft\lbrace3,4,5,6,7,8,9,10,11\mright\rbrace \\ \text{and} \\ A=\mleft\lbrace5,7,9,10\mright\rbrace \end{gathered}`

Then,

`\begin{gathered} A^C=U-A=\lbrace3,4,5,6,7,8,9,10,11\rbrace-\lbrace5,7,9,10\rbrace=\mleft\lbrace3,4,6,8,11\mright\rbrace \\ \Rightarrow A^C=\lbrace3,4,6,8,11\rbrace \end{gathered}`

Thus, the answer is {3,4,6,8,11}