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A boolean expression is a statement in logic or programming that evaluates to either true or false. These expressions are fundamental to control flow and decision-making within computer programs and logical systems. They are named after George Boole, the mathematician who developed Boolean algebra, the system of logic that underpins these expressions.

The simplest boolean expressions involve comparison operators. For example, "5 > 3" is a boolean expression that evaluates to true. Similarly, "x == 10" is a boolean expression where 'x' is a variable, and its truth value depends on the current value assigned to 'x'. Other common comparison operators include less than (<), greater than or equal to (>=), less than or equal to (<=), not equal to (!=), and equality (==).

Boolean expressions can be combined using logical operators to create more complex conditions. The primary logical operators are AND, OR, and NOT. The AND operator requires both conditions to be true for the overall expression to be true. For instance, "x > 0 AND x < 10" is true only if 'x' is a positive number less than ten. The OR operator requires at least one of the conditions to be true for the expression to be true. "IsSunny OR IsWarm" would be true if it's sunny, or if it's warm, or both. The NOT operator inverts the truth value of a condition; if a condition is true, NOT that condition is false, and vice versa.

Boolean expressions are crucial for implementing conditional statements like if-else structures, loops (like while loops), and switch statements, allowing programs to execute different code paths based on varying conditions. They are a cornerstone of computational logic and efficient program design.