Single Choice

If X $$=$$ (multiples of 2), Y $$=$$ (multiples of 5), Z $$=$$ (multiples of 10), then $$X \cap ( Y \cap Z )$$ is equal to

Amultiples of 10
Correct Answer
Bmultiples of 5
Cmultiples of 2
Dmultiples of 7

Solution

$$ We\quad can\quad write\quad the\quad given\quad sets\quad as\quad \\ X=\quad \left\{ 2,4,6,8,10,-----18,20,----28,30,---- \right\} \\ Y=\quad \left\{ 5,10,15,20,----30----40---- \right\} \\ Z=\quad \left\{ 10,20,30,40,----- \right\} \\ \therefore \quad Y\cap Z=\left\{ 10,20,30,---- \right\} \\ \therefore \quad X\cap \left( Y\cap Z \right) =\left\{ 10,20,30,----- \right\} =Z\\ \therefore \quad X\cap \left( Y\cap Z \right) =Z\quad \quad (Ans) $$

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