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The logical operators come from boolean algebra. Let's say you have two variables A and B. Then it would mean that:
A && B = True if A "AND" B is True. If one of them is False, the result is False.
A || B = True if A "OR" B is True. If one of them is True, the result is True.
The exclamation mark negates statements. Say A = True, then !A = False. Same counts for comparison A == B is True if A equals B. A != B, True if A unequals B