What does "implies and is implied by" refer to in logic?

The phrase "implies and is implied by" refers to a logical biconditional statement. In logic, this relationship is denoted by the symbol ↔. When you see a statement of the form "P ↔ Q," it means that P implies Q and Q implies P. This establishes a two-way conditional where both statements are equivalent; that is, both P and Q must either be true or false together.

Understanding this concept is crucial because it helps in constructing logical arguments, proofs, and understanding more complex logical relationships. The biconditional can often be understood in terms of necessary and sufficient conditions, where each statement provides the exact condition for the truth of the other. Therefore, recognizing that "implies and is implied by" directly corresponds with the biconditional relationship is fundamental in the study of logic.