lies are two kinds.
1. saying something has happened when actually it had not happened.
2. saying something not happened when actually it had happened.
Mathematically this LIE can be seen as an OR logical operator between truth T and false F.
At the same time, telling a truth as truth or false as false will actually make TRUTH.,which perfectly fits to the aforementioned definition for exclusive OR (XOR) logical operator.
so, XOR logical operator perfectly defines a LIE.
Truth table for XOR,
-----------------------------------
T T - - - - - - > F
T F - - - - - - > T
F T - - - - - -> T
F F - - - - - - > F
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