Let A = {x : x = 6n N) and B = {x : x = 9n, n ϵ N}, find A ∩ B.

Question:

Let $A=\{x: x=6 n \in N$ ) and $B=\{x: x=9 n, n \in N\}$, find $A \cap B$.

 

Solution:

$A=\{x: x=6 n \forall n \in N)$

As $x=6 n$ hence for $n=1,2,3,4,5,6 \ldots x=6,12,18,24,30,36 \ldots$

Hence $A=\{6,12,18,24,30,36 \ldots\}$

$B=\{x: x=9 n \forall n \in N)$

As $x=9 n$ hence for $n=1,2,3,4 \ldots x=9,18,27,36 \ldots$

Hence $B=\{9,18,27,36 \ldots\}$

$A \cap B$ means common elements to both sets

The common elements are $18,36,54, \ldots$

Hence $A \cap B=\{18,36,54, \ldots\}$

All the elements are multiple of 18

Hence $A \cap B=\{x: x=18 n \forall n \in N\}$

 

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