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If $\mathrm{A}=\{\mathrm{x}: \mathrm{x}$ is amultiple of 2$\}, \mathrm{B}=\{\mathrm{x}: \mathrm{x}$ is a multiple of 5$\}$ and $\mathrm{C}=\{\mathrm{x}: \mathrm{x}$ is a multiple of 10$\}$, then $\mathrm{A} \cap(\mathrm{B} \cap \mathrm{C})$ is equal to
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C
$\mathrm{A}=\{\mathrm{x}: \mathrm{x}$ ismultiple of 2$\}$ $\mathrm{B}=\{\mathrm{x}: \mathrm{x}$ ismultiple of 5$\}$
$C=\{x: x$ is multiple of 10
We know, multiples of 2 include multiples of 10 . $\therefore \mathrm{C} \subset \mathrm{A}$
Also, multiples of 5 include multiples of 10 . $\therefore \mathrm{C} \subset \mathrm{B}$
Also, $\mathrm{C}=\mathrm{A} \cap \mathrm{B}$
But $B=A \cap C, B \cap C=B$
$A \cap(B \cap C)=A \cap B=C$
$C=\{x: x$ is multiple of 10
We know, multiples of 2 include multiples of 10 . $\therefore \mathrm{C} \subset \mathrm{A}$
Also, multiples of 5 include multiples of 10 . $\therefore \mathrm{C} \subset \mathrm{B}$
Also, $\mathrm{C}=\mathrm{A} \cap \mathrm{B}$
But $B=A \cap C, B \cap C=B$
$A \cap(B \cap C)=A \cap B=C$
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