Its main utility is in representing the truth value statements, rather than the numeric quantities of ordinary algebra. It is used in the binary system in digital computers. The only truth values, true and false can be represented by the binary digits 1 and 0. The fundamental operators (Boolean logic) are "and,' "or," and "not." Thirteen other operators can be made up using a combination of these operators.
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The prototypical Boolean algebra; i.e. the Boolean algebra defined over the Boolean domain, has two elements in it: 0 and 1. For more information about Boolean algebra, please refer to the related link below.
Algebra is a very broad topic covering all sorts of things, including Boolean algebra. Boolean algebra in itself is the study of a variable called "Boolean." This variable can only take two values: true and false. See 'related links' for more information.
Algebra is related to medical technology because you can't do medical technology as much if you don't know Algebra. Because Algebra makes it easier.
Algebra and Geometry are not related to each other directly, however in higher levels of math (Trigonometry and Calculus) you will use both very frequently
It is Arithmetica, by Diophantus of Alexandria, who is generally considered the father of algebra, that may be the first writing on algebra. But there is a bit of debate over who the father of algebra is. Use the link below to the related question.