Question

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
\[
  A)\{ 6,12,18,.....\} \\
  B)\{ 3,6,9,12,......\} \\
  C)\{ 3,9,15,21,.....\} \\
  D){\text{none of the above}} \\
\]

Answer 1

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.