http://gametheory101.com/courses/logic-101/ This lecture introduces the biconditional logical operator, equivalent to the phrase "if and only if" in English. Biconditionals are logic's version of an equals sign. If one part of a biconditional is true, then the other part is true as well. But if one part is false, the other part is false as well. "If and only if" thus has a distinct logical meaning. Be careful not to use those words as a fancier way of say "if" or "only if," as you won't be saying what you are actually trying to say.