First slide

Operations on Sets

Question

If $A = {2 x : x \in N}, B = {3 x : x \in N}$ and $C = {5 x : x \in N)$ then $A \cap (B \cap C)$ is equal to

Moderate

A

${15, 30, 45, \dots}$
B

${10, 20, 30 \dots}$
C

$\{30, 60, 90, \dots\}$
D

${7, 14, 21 \dots}$

Solution

$\begin{array}{l} (A \cap B) \cap C = {2 \times 3 \times 5 x : x \in N} \\ = {30 x : x \in N} \end{array}$

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