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The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), [2] and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of ...
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.
material biconditional (material equivalence) if and only if, iff, xnor propositional logic, Boolean algebra: is true only if both A and B are false, or both A and B are true. Whether a symbol means a material biconditional or a logical equivalence, depends on the author’s style.
Logical biconditional; Logical equality; ≡ the iff symbol (U+2261 IDENTICAL TO) ∷ the a is to b as c is to d symbol (U+2237 PROPORTION) ⇔ the double struck biconditional (U+21D4 LEFT RIGHT DOUBLE ARROW) ↔ the bidirectional arrow (U+2194 LEFT RIGHT ARROW)
In other words, the contrapositive is logically equivalent to a given conditional statement, though not sufficient for a biconditional. Similarly, take the statement " All quadrilaterals have four sides, " or equivalently expressed " If a polygon is a quadrilateral, then it has four sides.
Biconditional introduction All rules use the basic logic operators. A complete table of "logic operators" is shown by a truth table , giving definitions of all the possible (16) truth functions of 2 boolean variables ( p , q ):
An abbreviation for "if and only if," denoting a biconditional logical connective indicating mutual implication. ignoratio elenchi A logical fallacy where an argument misses the point or addresses an issue different from the one that was raised, also known as missing the point. image The set of all outputs of a function from a given set of inputs.
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true inputs is odd ...