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  2. If and only if - Wikipedia

    en.wikipedia.org/wiki/If_and_only_if

    The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...

  3. Logical biconditional - Wikipedia

    en.wikipedia.org/wiki/Logical_biconditional

    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.

  4. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    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. x + 5 = y + 2 ⇔ x + 3 = y {\displaystyle x+5=y+2\Leftrightarrow x+3=y}

  5. Contraposition - Wikipedia

    en.wikipedia.org/wiki/Contraposition

    The symbol for the biconditional ("↔") signifies the relationship between the propositions is both necessary and sufficient, and is verbalized as "if and only if", or, according to the example "If P, then Q 'if and only if' if not Q, then not P".

  6. Congruence (geometry) - Wikipedia

    en.wikipedia.org/wiki/Congruence_(geometry)

    In analytic geometry, congruence may be defined intuitively thus: two mappings of figures onto one Cartesian coordinate system are congruent if and only if, for any two points in the first mapping, the Euclidean distance between them is equal to the Euclidean distance between the corresponding points in the second mapping.

  7. Logical equivalence - Wikipedia

    en.wikipedia.org/wiki/Logical_equivalence

    This statement expresses the idea "' if and only if '". In particular, the truth value of p ↔ q {\displaystyle p\leftrightarrow q} can change from one model to another. On the other hand, the claim that two formulas are logically equivalent is a statement in metalanguage , which expresses a relationship between two statements p {\displaystyle ...

  8. Logical conjunction - Wikipedia

    en.wikipedia.org/wiki/Logical_conjunction

    In high-level computer programming and digital electronics, logical conjunction is commonly represented by an infix operator, usually as a keyword such as "AND", an algebraic multiplication, or the ampersand symbol & (sometimes doubled as in &&). Many languages also provide short-circuit control structures corresponding to logical conjunction.

  9. Validity (logic) - Wikipedia

    en.wikipedia.org/wiki/Validity_(logic)

    Many techniques are employed by logicians to represent an argument's logical form. A simple example, applied to two of the above illustrations, is the following: Let the letters 'P', 'Q', and 'S' stand, respectively, for the set of men, the set of mortals, and Socrates. Using these symbols, the first argument may be abbreviated as: All P are Q.