Logical equality (also known as biconditional) is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false or both operands are true.
What is a biconditional statement? Learn the definition, view biconditional statement examples, and learn how to write a biconditional statement step-by-step.
What Is a Biconditional? "It is daytime if and only if it is not nighttime." This statement does more than just "if it's daytime, then it's not nighttime" — it also says the reverse: "if it's not nighttime, then it's daytime."
A biconditional is a logical connective that represents a relationship between two propositions where both propositions are either true or false simultaneously.
Whenever we have two statements that perfectly match in truth value (both true or both false), we say they're equivalent, or in logical terms, related by a biconditional.
A biconditional is true when both parts are true or both are false: when they have the same truth value. It is false when one part is true and the other is false. It is sometimes written as if and only if. Example: You get cake if and only if you eat your vegetables.
biconditional establishes that two statements are logically equivalent - they always have the same truth value. when one is true, the other must be true; when one is false, the other must be false. P ↔ Q ≡ Q ↔ P. unlike implication, biconditional is symmetric - order doesn’t matter.
A biconditional is a logical conditional statement in which the antecedent and consequent are interchangeable. A biconditional is written as p ↔ q and is translated as “p if and only if q”.
In logic and related fields such as mathematics and philosophy, " if and only if " (often shortened as " iff ") is paraphrased by the biconditional, a logical connective [1] between statements. The biconditional is true in two cases, where either both statements are true or both are false.
