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More # If A = $\{ x \in {\rm N}:{\text{x is a multiple of }}3\}$ and B = $\{ x \in {\rm N}:{\text{x is a multiple of 6}}\}$ then A-B is equals to$A)\{ 6,12,18,.....\} \\ B)\{ 3,6,9,12,......\} \\ C)\{ 3,9,15,21,.....\} \\ D){\text{none of the above}} \\$

Last updated date: 30th Mar 2023
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Hint: Here to proceed the solution we need to know the multiples of 3 and 6. Make set A and set B as per given condition.

Here we are given with two sets where with the condition, Where
A = $\{ x \in {\rm N}:{\text{x is a multiple of }}3\}$
Here set A is a multiple of 3 which are natural numbers.
Then $A = \{ 3,6,9,12,15,18,.......\}$
$B = \{ x \in {\rm N}:{\text{x is a multiple of 6}}\}$
Here set B is a multiple of 6 which are natural numbers.
Then $B = \{ 6,12,18,24,.....\}$

Now we got both the values of set A and set B
Then
$A - B = \{ 3,6,9,12,15,18,.....\} - \{ 6,12,18,24,30,....\} \\ A - B = \{ 3,9,12,15,21,.....\} \\$
Here A-B means we have removed the element of set B from set A.
Option C is the correct answer.

NOTE: In these problems first we have to find the value of set A by given condition and in the same way we have to find the values of set B .Later we have to find A-B which means we have to subtract values of set B from set A. In this type of problem mainly we have to focus on the conditions given to the sets because different sets have different conditions.