Question

How was Boolean logic invented?

Answer 1

Hint: Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted $$1$$ and $$0$$ respectively. They do not behave like the integers $$1$$ and $$0$$ . A sequence of bits is commonly used for such functions.

Complete answer: British mathematician George Boole invented Boolean logic in the $$19th$$ Century. Boolean logic can also be called Boolean algebra. In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted $$1$$ and $$0$$ respectively. They do not behave like the integers $$1$$ and $$0$$ for which $$1+1=2$$ but may be identified with the elements of the two-element field GF $$\left(2\right)$$ that is, integer arithmetic modulo $$2$$ for which $$1+1=0$$ . Addition and multiplication then play the Boolean roles of XOR (exclusive-or) and AND (conjunction), respectively. Boolean algebra also deals with functions which have their values in the set $$\left\{0,1\right\}$$. A sequence of bits is commonly used for such functions.
The basic operations of Boolean algebra are as follows:
1.AND (conjunction) satisfies x AND y $$=1$$ if $$x=y=1$$ and x AND y $$=0$$ otherwise.
2.OR (disjunction) satisfies x OR y $$=0$$ if $$x=y=0$$ and x OR y $$=1$$ otherwise.
3.NOT (negation) satisfies NOT x $$=0$$ if $$x=1$$ and NOT x $$=1$$ if $$x=0$$ .

Note:
Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted $$1$$ and $$0$$ respectively. They do not behave like the integers $$1$$ and $$0$$ . A sequence of bits is commonly used for such functions.