Definition of set in phrasal verb from the Oxford Advanced Learner's Dictionary

 

set in

 phrasal verb
phrasal verb
 
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Phrasal Verbs
(of rain, bad weather, infection, etc.) to begin and seem likely to continue The rain seemed to have set in for the day.

set something in something

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set something into something

 
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[usually passive] to fasten something into a flat surface so that it does not stick out from it a plaque set into the wall
See the Oxford Advanced American Dictionary entry: set in