Define Bi-conditional.

The biconditional, symbolized by the double arrow (↔), represents a logical relationship between two propositions where they are both true or both false. It is a statement asserting that the truth of one proposition is equivalent to the truth of another. The biconditional is a compound statement often used in formal logic and mathematics.

In a biconditional statement "p ↔ q," both p and q have the same truth value. If p is true, then q must be true, and if p is false, then q must be false. The biconditional expresses a two-way relationship: the truth of one proposition implies the truth of the other, and vice versa.

For example, let p represent "It is snowing" and q represent "The ground is covered in snow." The biconditional "p ↔ q" asserts that if it is snowing, then the ground is covered in snow, and conversely, if the ground is covered in snow, then it is snowing.

The biconditional is a powerful tool in expressing equivalence and mutual dependence between propositions. It is commonly used in mathematics, logic, and computer science to formalize relationships where two conditions are intrinsically linked, and their truth values are interdependent.