If for a positive integer a- aN - ax- x - and 13N - 7N - kN- then the value of k is

13N = {13x: x ∈ℕ} ={13, 26, 39, …} Collection of multiples of 13 Similarly, 7N = {7x: x ∈ℕ} ={7, 14, 21, …} Collection of multiples of 7 So, 13N ∩ 7N ...

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Standard XII

Mathematics

Intersection of Sets

If for a posi...

Question

If for a positive integer $a, a N = {a x : x \in N}$ and $13 N \cap 7 N = k N$ , then the value of $k$ is

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Solution

$13 N = {13 x : x \in N} = {13, 26, 39, \dots}$
Collection of multiples of $13$

Similarly, $7 N = {7 x : x \in N}$
$= {7, 14, 21, \dots}$
Collection of multiples of $7$

So, $13 N \cap 7 N$ contains multiples common to both $7$ and $13$ .
i.e., $13 N \cap 7 N \to$ Collection of multiples of $91$ .
$∴ 13 N \cap 7 N = {91 x : x \in N} = 91 N$

Hence, $k = 91$

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If for a positive integer a,aN={ax:x∈N} and 13N∩7N=kN, then the value of k is

13N={13x:x∈N} ={13,26,39,…} Collection of multiples of 13 Similarly, 7N={7x:x∈N} ={7,14,21,…} Collection of multiples of 7 So, 13N∩7N contains multiples common to both 7 and 13. i.e., 13N∩7N→ Collection of multiples of 91. ∴13N∩7N={91x:x∈N}=91N Hence, k=91

If for a positive integer $a, a N = {a x : x \in N}$ and $13 N \cap 7 N = k N$ , then the value of $k$ is