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Because computers uses binary as its language. And programs are representation of logic.
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 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.
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.
One use of Boolean algebra is to minimize any function or logic gate.