For the universal set, $U=\{q, r, x, y, z\}$, complete the parts below. Write your answers in roster form or as $\varnothing$.
(a) Suppose $A=\{q, x, y, z\}$. Then what is $A^{\prime}$ ?
\[
A^{\prime}=\square
\]
(b) Suppose we know that $B^{\prime}=\{r, y\}$. Then what would $B$ have to be?
\[
B=\square
\]
Answer
Therefore, \(B=\{q, x, z\}\)
Step 1 ：Given the universal set \(U=\{q, r, x, y, z\}\)
Step 2 ：Given the set \(A=\{q, x, y, z\}\)
Step 3 ：The complement of a set A, denoted by \(A'\), is the set of all elements in the universal set U that are not in A
Step 4 ：So, \(A'\) is the set of all elements in U that are not in A
Step 5 ：Therefore, \(A'=\{r\}\)
Step 6 ：Similarly, given that \(B'=\{r, y\}\)
Step 7 ：Then B is the set of all elements in U that are not in \(B'\)
Step 8 ：Therefore, \(B=\{q, x, z\}\)
