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Simply so, do jellyfish know they exist?
The thing is, while jellyfish don't have a brain or central nervous system, they do have a very basic set of nerves at the base of their tentacles. These nerves detect touch, temperature, salinity etc. and the jellyfish reflexively respond to these stimuli.
Furthermore, can Jellyfish think? Jellyfish don't have brains So how does a jellyfish live without these vital organs? And they respond to the changes in their environment around them using signals from a nerve net just below their epidermis - the outer layer of skin - that is sensitive to touch, so they don't need a brain to process complex thoughts.
Keeping this in view, do jellyfish feel emotion?
Jellyfish are very similar to anemones, so they display a very similar response. So, the detailed answer to your question is that jellyfish do not feel pain the in the same way we humans do. However, they do have the ability to sense and respond to aversive stimuli.
Can jellyfish remember?
According to this wikipedia article, box jellyfish have short memories and a limited ability to learn.