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  4. Let X and Y be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number), then (X ∩ Y) =

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Q. Let $X$ and $Y$ be the sets of all positive divisors of $400$ and $1000$ respectively (including $1$ and the number), then $(X \cap Y) =$

Sets

Solution:

$X$ and $Y$ be set of all divisors of $400$ and $1000$.
So $X = \{1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400\}$
$Y = \{1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, .... 1000\}$
$X \cap Y = \{1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200\}$
$12$ elements are common in both the sets.
$\Rightarrow n(X \cap Y) = 12$