It is used in science and proofs of proofs in maths, taking an example:
Hypothesis: Bananas are red.
(There exists) x x (is an element of) Red (and) Banana
Banana (implies) Red
(not) Red (implies) (not) Banana
If a yellow banana is found,
(There exists) y y(is an element of)Banana (therefore) y(is an element of) Red
There is a contradiction, as the banana must be red, but it is yellow.
The above is not the only use, but Boolean algebra exclusively contains symbols of (not), (and), and (or).
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AND, OR, and NOT are the basic operators in Boolean Algebra.
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Boolean algebra is a division of mathematics that deals with operations on logical values and incorporates binary variables.
A Boolean variable is a variable from Boolean algebra having one of only two values.