First slide

Operations on Sets

Question

$If a N = {a x : x \in N}, then the set 3 N \cap 7 N is$

Easy

A

21N
B

10N
C

4N
D

None of these

Solution

$3 N = {x \in N : x is a multiple of 3}$
$\begin{array}{rcl} 7 N & = & {x \in N : x is a multiple of 7} \\ 3 N \cap 7 N & = & {x \in N : x is a multiple of 3 and 7} \\ = & {x \in N : x is a multiple of 21} = 21 N \end{array}$

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