Question

if Na is (a,n:n E N), then N6 union N8=???

Answer 1

Hey There!!



Here Let us first understand what the statement means:


$N_a = \{a.n : n\in N\}$


This simply means that $N_a$ is the set of multiples of a. You can also write it as follows:


$N_a = \{a,2a,3a,4a,5a,...\}$


So, we have:

$N_6 = \{6,12,18,24,30,36,42,48,54,60,...\} \\ \\ N_8 = \{8,16,24,32,40,48,56,64,72,80,...\}$


Now, we just have to find the intersection of the two elements. 

In other words, we have to find the set, which contains common multiples of 6 and 8. 

All common multiples of 6 and 8 will be multiples of the LCM of 6 and 8.

For 6 and 8, LCM = 24.

All common multiples of 6 and 8 will be multiples of 24.

We can see that

$N_6\cap N_8 = \{24,48,72,96,...\} \\ \\ \implies \boxed{N_6\cap N_8 = N_{24}}$


Thus, your answer is Option (3) $N_{24}$



Hope it helps
Purva
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