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

• A. $\{2,4,6\}$
• B. $\left\{8\right\}$
• C. $\{2,4,6,8\}$
• D. $\varphi$

Answer: (B)

Verified step by step guidance

1. Identify the sets given: \(A = \left\lbrace 2, 4, 6, 8 \right\rbrace\), \(B = \left\lbrace 4, 8, 12, 16 \right\rbrace\), and \(C = \left\lbrace 8 \right\rbrace\).
2. Recall that the intersection of two sets, for example \(A \cap C\), consists of all elements that are common to both sets \(A\) and \(C\).
3. List the elements of set \(A\) and set \(C\) side by side to compare: \(A = \{2, 4, 6, 8\}\) and \(C = \{8\}\).
4. Determine which elements appear in both \(A\) and \(C\). Since \$8\( is the only element in \)C\( and it is also in \)A$, it is the common element.
5. Write the intersection set as \(A \cap C = \left\lbrace 8 \right\rbrace\), which contains all elements common to both sets.