Let $U=\{a, b, c, d, e, f, g\}, A=\{c, f, g\}, B=\{a, f, g\}$, and $C=\{a, b, c, d\}$. Find the following set. $A \cup(B \cap C)$
Select the correct choice below and fill in any answer boxes within your choice.
A. $A \cup(B \cap C)=\{[\}$
B. $A \cup(B \cap C)=\varnothing$
Answer
So, the final answer is \(\boxed{\{a, c, f, g\}}\).
Step 1 ：First, we need to find the intersection of sets B and C. The intersection of two sets is the set of elements that are common to both sets. So, we have \(B \cap C = \{a, f, g\} \cap \{a, b, c, d\} = \{a\}\).
Step 2 ：Next, we need to find the union of sets A and \(B \cap C\). The union of two sets is the set of elements that are in either set. So, we have \(A \cup (B \cap C) = \{c, f, g\} \cup \{a\} = \{a, c, f, g\}\).
Step 3 ：So, the final answer is \(\boxed{\{a, c, f, g\}}\).
