[Comevius]

They are not independent, if a partition occurs you can give up consistency for availability. For example if you have a database server and it becomes unavailable, the best you can do is eventual consistency, and if you do you no longer have a single source of truth, until eventually your causality protocol reestablishes it.

For example the client can decide to give up availability if the server is unavailable, or give up consistency by accepting writes, which later have to be merged back somehow handling any conflict that wouldn't occur otherwise.

https://en.wikipedia.org/wiki/PACELC_theorem