Let $$\begin{array} { l }
U = \{ 1,2,3,4,5,6,7,8,9,10 \} \
A = \{ 2,4,6,8 \} \
B = \{ 3,7 \} \
C = \{ 2,3,6,7,10 \}
\end{array}$$ List all the members of the set. $A \cap \overline { B \cup C }$
A) $\{ 2,6 \}$
B) $\{ 4,6 \}$
C) $\{ 4,8 \}$
D) $\{ 2,4,6 \}$
E) $\varnothing$

Question

Let $$\begin{array} { l } 
U = \{ 1,2,3,4,5,6,7,8,9,10 \} \
A = \{ 2,4,6,8 \} \
B = \{ 3,7 \} \
C = \{ 2,3,6,7,10 \}
\end{array}$$ List all the members of the set. $A \cap \overline { B \cup C }$
A) $\{ 2,6 \}$
B) $\{ 4,6 \}$
C) $\{ 4,8 \}$
D) $\{ 2,4,6 \}$
E) $\varnothing$

Quizplus · Accepted Answer

To find $A \cap \overline { B \cup C }$, first find $B \cup C = \{ 2,3,6,7,10 \}$. The complement of $B \cup C$ in $U$, $\overline { B \cup C }$, is $\{ 1,4,5,8,9 \}$. The intersection of $A$ and $\overline { B \cup C }$ is $\{ 4,8 \}$, which are the elements present in both $A$ and $\overline { B \cup C }$.

Let U={1,2,3,4,5,6,7,8,9,10}A={2,4,6,8}B={3,7}C={2,3,6,7,10}\begin{array} { l } U = \{ 1,2,3,4,5,6,7,8,9,10 \} \\A = \{ 2,4,6,8 \} \\B = \{ 3,7 \} \\C = \{ 2,3,6,7,10 \}\end{array}U={1,2,3,4,5,6,7,8,9,10}A={2,4,6,8}B={3,7}C={2,3,6,7,10}​

Let $\begin{array} { l } U = \{ 1,2,3,4,5,6,7,8,9,10 \} \\A = \{ 2,4,6,8 \} \\B = \{ 3,7 \} \\C = \{ 2,3,6,7,10 \}\end{array}$