First slide

Operations on Sets

Question

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

Easy

A

21 N
B

10 N
C

4 N
D

None of these

Solution

$3 N = \{x \in N : x is a multiple of 3\}$
$7 N = \{x \in N : x is a multiple of 7\}$
$∴ 3 N \cap 7 N = \{x \in is a multiple of 3 and 7\}$
$= \{x \in N : x is a multiple of 3 and 7\}$
$= \{x \in N : x is a multiple of 21\} = 21 N .$

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