D-separation multiple paths, active and inactive, is A ⊥ B | C ? [Q]

I’m learning about D-separation and the rules are somewhat alien to me. But what I’ve gathered is, you find multiple paths connecting A and B via C, where C is a set of nodes. From these paths you identify all triples along each path. Depending on whether or not a variable is observed plays an important role in whether or not a triple is active, and thus the whole path is active.

To the best of my ability, I’ve determined that one path is active and the other is inactive. Does this make A ⊥ B | C ? My understanding as of now is that it only takes one inactive path to verify the above to be true.

Because of the rules on this a picture cannot be added, so I’ve linked a graph that shows the nodes and paths.

https://stats.stackexchange.com/questions/439174/is-a-%e2%8a%a5-b-c-where-one-path-active-but-another-inactive

I’d love to build intuitions for why the rules are the way that they are; but my goal is a bit more humble as now, simply memorizing the rules/use cases for now. Added context or intuition would be appreciated but I’m mostly interested in verifying that my analysis is correct.

submitted by /u/jbuddy_13
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Nevin Manimala

Nevin Manimala is interested in blogging and finding new blogs https://nevinmanimala.com

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