It's possible to perpetrate a good deed, but not likely. That's because perpetrate means to commit or be responsible for something usually something mischievous or bad.
To do or perform; to carry through; to execute, commonly in a bad sense; to commit (as a crime, an offense); to be guilty of;
Verb
perform an act, usually with a negative connotation; "perpetrate a crime"; "pull a bank robbery"
v. t.
To do or perform; to carry through; to execute,
commonly in a bad sense; to commit (as a crime, an offense); to be
guilty of; as, to perpetrate a foul deed.
Perpetrate
What the worst perpetrate, or best endure.
To do or perform; to carry through; to execute, commonly in a bad sense; to commit (as a crime, an offense); to be guilty of;
Usage Examples
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