Because computers uses binary as its language.
And programs are representation of logic.
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Boolean logic can be thought of as "0 and 1" logic, or "True or False" logic. Boolean math started out as "True or False" expressions. In computers, the bits stored in memory are interpreted as either a '0' or a '1' (binary numbers). Computer scientists (usually, though you can prove out the concept either way) map '0' = FALSE and '1' = 'TRUE', and thus the operations and decisions made in a computer can be expressed/evaluated as Boolean logic/math expressions.
He invented what is now simply known as Boolean logic. It is what is used in modern computers.
The connection stems from the fact that in Boolean logic binary numbers are used and these are used in computers as well. That reminds of a joke you may have heard. There are only 10 kinds of people: -those who understand binary; -those who don't
Boolean Algebra is the study of the algebra of logic whilst Mathematical logic is a way of applying Boolean algebra. Other applications include set theory, digital logic and probability.
Boolean algebra is a mathematical method used to describe the behavior and operation of digital logic. Boolean descriptions and relationships can help us design logic and predict the behavior of more complex digital systems.