Given $A=\{2,4,6,8\}$, $B=\{4,8,12,16\}$, $C=\left\{8\right\}$, find the following:
(B) $A\cup B$

• A. $\(\left\[\lbrace\)2,4,6,8,12,16\(\right\]\rbrace\)$
• B. $\(\left\[\lbrace\)4,8\(\right\]\rbrace\)$
• C. $\(\left\[\lbrace\)2,6,12,16\(\right\]\rbrace\)$
• D. $\(\phi\)$

Answer: (A)

Verified step by step guidance

1. Identify the two sets given: \(A = \left\lbrace 2,4,6,8 \right\rbrace\) and \(B = \left\lbrace 4,8,12,16 \right\rbrace\).
2. Recall that the union of two sets, denoted \(A \cup B\), includes all elements that are in \(A\), or in \(B\), or in both.
3. List all elements from set \(A\): \$2, 4, 6, 8$.
4. Add all elements from set \(B\) that are not already in \(A\): \$12, 16$.
5. Combine these elements into one set without duplicates: \(\left\lbrace 2,4,6,8,12,16 \right\rbrace\).