Do you remember set theory?

Probability Level 1

If $X$ and $Y$ are two sets, $X \cap (Y \cup X)^c$ is equal to

Details and assumptions :
$\rightarrow$ $\cap$ represents intersection.
$\rightarrow$ $\cup$ represents union.
$\rightarrow$ $X^c$ represents compliment of set $X$ .

Y

X

\emptyset

X \cup Y

X \cap Y

1 solution

Akhil Bansal
Aug 12, 2015

$\Rightarrow$ X $∩$ $(Y ∪ X)^c$
$\Rightarrow$ X $∩$ $(Y^c∩X^c)$
$\Rightarrow$ ( $X ∩ Y^c$ ) $∩$ $(X∩X^c)$
$\Rightarrow$ ( $X ∩ Y^c$ ) $∩$ $\phi$
$\Rightarrow$ $\boxed{\phi}$

More simply, we can say that $X \cap (Y' \cap X') = Y' \cap (X \cap X') = Y' \cap \emptyset$ since set intersections are associative and commutative.

Jaydee Lucero - 5 years, 7 months ago

Agree with Jaydee

Darko Doko - 11 months ago

Do you remember set theory?

1 solution

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