Boolean algebra is a mathematical structure that deals with binary variables and logical operations. It is named after mathematician and logician George Boole, who developed the algebraic system in the mid-19th century.

In Boolean algebra, variables can only take on two values: true (represented by 1) or false (represented by 0). The algebraic operations in Boolean algebra include logical AND, OR, and NOT.

The logical AND operation, denoted by the symbol “∧” or “*”, returns true if both operands are true, and false otherwise. For example, 1 ∧ 1 = 1, 1 ∧ 0 = 0, 0 ∧ 1 = 0, and 0 ∧ 0 = 0.

The logical OR operation, denoted by the symbol “∨” or “+”, returns true if at least one of the operands is true, and false otherwise. For example, 1 ∨ 1 = 1, 1 ∨ 0 = 1, 0 ∨ 1 = 1, and 0 ∨ 0 = 0.

The logical NOT operation, denoted by the symbol “¬” or “’”, returns the opposite value of the operand. For example, ¬1 = 0 and ¬0 = 1.

Boolean algebra also includes other operations such as XOR (exclusive OR), NAND (NOT AND), NOR (NOT OR), and XNOR (exclusive NOR), which can be derived from the basic operations.

Boolean algebra is widely used in computer science and digital electronics to represent and manipulate logical expressions and circuits. It provides a formal system for reasoning about logical statements and is the foundation of Boolean logic, which underlies the design and operation of digital computers.