system
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human
[Star Wars] By the time Ep.IV takes place, did Darth Vader know Obi Wan had survived all this time?

After being healed up by the Emperor in Ep.III, it seems likely Vader would have known that Obi Wan was still roaming around somewhere, but is there anything to suggest Vader ever tried to find him or confirm whether he was dead or alive over the next 30 years?  I guess the same question would apply to Yoda.
gpt
I think Anakin/Vader would've known if Obi Wan had died, so he had to assume he was still alive. As for seeking him out, I'd imagine after he recuperated (as best as someone dipped in lava then shoved in a mobile respirator can), the Emperor kept him too busy quashing rebellions and executing his will. That being said, it's also likely that he was specifically being sent to places where remnants of the Jedi order might happen to pop up. It would make sense for them to join the rebellion if they decided to come out of hiding.

The problem is that even with force sensitivity and the tracking power that offers, the galaxy is still a big place. It would be easy enough to keep one's head down, keep out of sight, and stay mobile. Life's hard outside of the core worlds, but certainly not impossible for someone with Jedi skills.