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Boolean algebra, also known as Boolean logic, is a branch of algebra that deals with variables that can take on only two values: true or false. It is named after George Boole, who introduced the concept in the mid-19th century. Boolean algebra is fundamental to computer science and digital electronics, as it forms the basis for digital circuits and logic gates.

The basic operations in Boolean algebra are AND, OR, and NOT. The AND operation, denoted by ∧, returns true only if both operands are true. The OR operation, denoted by ∨, returns true if at least one of the operands is true. The NOT operation, denoted by ¬, returns the opposite of the operand's value.

Boolean algebra also includes the concepts of tautology and contradiction. A tautology is a Boolean expression that is always true, regardless of the values of its variables. A contradiction is a Boolean expression that is always false.

Boolean algebra can be extended to include additional operations and concepts, such as XOR (exclusive OR), NAND (NOT AND), and NOR (NOT OR). These operations are used in various applications, including digital circuit design, computer programming, and artificial intelligence.

Boolean algebra is a powerful tool for analyzing and manipulating logical expressions. It provides a systematic way to simplify and optimize logical circuits, leading to more efficient and reliable digital systems.