English example sentences with "under the illusion"

I think Mark's under the illusion that he will be the new director.
Translate from English to Spanish

Everybody is fighting each other under the illusion that it is the "other people" that are causing the problem. We don't realize that we are all in the same boat. We are all suffering from the absence of a system that can pull us together and assure us that the results of each person's work will come back to him and enhance his life in some way.
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