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Logical Implication

Description: Logical implication is a fundamental concept in logic and mathematics, stating that one statement (known as the antecedent) follows logically from another statement (known as the consequent). It expresses the relationship between propositions, asserting that if the antecedent is true, then the consequent must also be true.

Sense 1: In logic, the term "logical implication" refers to the relationship between two statements, where one statement logically entails the other. It is denoted by the symbol '⇒' or the phrase "if...then." The truth table for logical implication shows that if the antecedent (p) is true and the consequent (q) is false, then the implication is false; otherwise, it is true.

Example: If it is raining (p), then the ground is wet (q).

Related Products: Logic Books

Sense 2: In mathematics, logical implication is used to define mathematical statements and proofs. It helps establish relationships between mathematical principles and allows for the construction of logical arguments in various mathematical disciplines.

Example: If a number is divisible by 6, then it is divisible by both 2 and 3.

Related Products: Mathematics Books