Logical equivalence refers to having the same truth condition in logic. These two propositions are logically equivalent, which means that they have the same truth table, that is, their truth values are the same under all possible circumstances. Logical equivalence is usually expressed by logical operators, such as logical AND, logical OR, implication, etc.

Mathematical equivalence refers to having the same nature or relationship in mathematics. Two mathematical objects (such as equations, inequalities, sets, etc. ) are mathematically equivalent, which means that they have the same result or property under certain mathematical properties or relationships. Mathematical equivalence is usually expressed and proved by mathematical symbols and reasoning methods.

Generally speaking, logical equivalence focuses on the truth relationship between propositions, while mathematical equivalence focuses on the nature or relationship between mathematical objects. Logical equivalence is a concept of logic, which is used to study the logical relationship of propositions. Mathematical equivalence is a mathematical concept, which is used to study the properties and relationships of mathematical objects.