Define sets $U, A, B$, and $C$ as shown below. Find $A^{\prime} \cap\left(B \cup C^{\prime}\right)$. \[ U=\{a, b, c, d, e, f, g, h\} \quad A=\{a, g, h\} \quad B=\{b, g, h\} \quad C=\{b, c, d, e, f\} \] Select the correct choice below and, if necessary, fill in the answer box within your choice. A. (Use a comma to separate answers as needed. Type each answer only once.) B. $A^{\prime} \cap\left(B \cup C^{\prime}\right)=\varnothing$

Step 1 ：Define the sets U, A, B, and C as U = {a, b, c, d, e, f, g, h}, A = {a, g, h}, B = {b, g, h}, and C = {b, c, d, e, f}.

Step 2 ：Find the complement of set A, denoted as \(A^\prime\), which includes all elements in the universal set U that are not in A. So, \(A^\prime\) = {b, d, f, c, e}.

Step 3 ：Find the complement of set C, denoted as \(C^\prime\), which includes all elements in the universal set U that are not in C. So, \(C^\prime\) = {g, h, a}.

Step 4 ：Find the union of set B and \(C^\prime\), denoted as \(B \cup C^\prime\), which includes all elements that are in either B or \(C^\prime\), or in both. So, \(B \cup C^\prime\) = {b, h, g, a}.

Step 5 ：Find the intersection of \(A^\prime\) and \(B \cup C^\prime\), denoted as \(A^\prime \cap (B \cup C^\prime)\), which includes all elements that are in both \(A^\prime\) and \(B \cup C^\prime\). So, \(A^\prime \cap (B \cup C^\prime)\) = {b}.

Step 6 ：Final Answer: \(A^\prime \cap (B \cup C^\prime)\) = \(\boxed{\{b\}}\)