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- [mathematics] A logical operator used in the formulation of a Boolean expression. Common Boolean operators include AND, which specifies a combination of conditions (A and B must be true); OR, which specifies a list of alternative conditions (A or B must be true); NOT, which negates a condition (A but not B must be true); and XOR (exclusive or), which makes conditions mutually exclusive (A or B may be true but not both A and B).