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

Question

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

Quizplus · Accepted Answer

The complement of a set $A$ is the set of all elements in the universal set that are not in $A$. In this case, $\bar{A}$ is the set of all elements in $U$ that are not in $A$. Therefore, we can eliminate choices A and D because they both contain the element $3$, which is not in $\bar{A}$. We can eliminate choice E because the complement of a set should not result in the empty set. That leaves us with choices B and C. However, choice B includes the elements in $U$ that are not in $A$ and also the elements in $B$ that are not in $A$. Therefore, we eliminate choice B and select choice C as the best choice, which only includes the elements in $U$ that are not in $A$.

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

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