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Does the following rule hold?

$\left\{ \begin{array}\\ X \perp Y \\ X \perp Z \end{array} \right. \Rightarrow X \perp Y,Z $

If it does not hold, what is a counterexample?

Karolis Koncevičius
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alireza
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  • Consider a dataset with "tea_sweet", "sugar_added", "cup_stirred". It is plausible that "tea_sweet" is independent of "cup_stirred" and "sugar_added", but knowing both "sugar_added" and "cup_stirred" will give you a high certainty of the tea being sweet. – Arun Jose Sep 21 '21 at 06:41

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