The claim is not implied. On the path $A\leftrightarrow Y\leftarrow X$, $Y$ is a <collider>, and conditioning on $Y$ opens that path. Equivalently, conditioning on the common effect $Y$ can induce <collider bias> between $A$ and $X$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 221 / 3 / iii / a / Solution

On a path in a directed graph, an interior vertex is a collider when both adjacent path edges have arrowheads pointing into it. A path through a collider is blocked unless that collider or one of its descendants is conditioned upon.


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 Incoming links: Collider