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1. and
Boolean logic operator where all values in the argument must be true in order for the whole statement to be true. Often denoted with '&' ('&&' in programming languages).
If x=1 and y=0, then

(x AND y) = 0
2. or
Boolean logic operator where at least one argument in the expression must be true in order for the whole statement to be true. Often denoted with '+' ('||' in programming languages).
if x=1 and y=0, then

(x OR y) = 1
3. not
Boolean logic operator that inverts a given value. Often denoted with '~' ('!' in programming languages).
(NOT a) AND (NOT a') = a
4. nor
Boolean logic operator that is equivalent to an AND function with all of its input values inverted. It has the following truth table:

X Y | Out
------------
0 0 | 1
0 1 | 0
1 0 | 0
1 1 | 1
x NOR y = (NOT x) AND (NOT y)
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