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  2. If and only if - Wikipedia

    en.wikipedia.org/wiki/If_and_only_if

    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 ...

  3. English conditional sentences - Wikipedia

    en.wikipedia.org/wiki/English_conditional_sentences

    In English language teaching, conditional sentences are often classified under the headings zero conditional, first conditional (or conditional I), second conditional (or conditional II), third conditional (or conditional III) and mixed conditional, according to the grammatical pattern followed, particularly in terms of the verb tenses and ...

  4. 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 bidirectional implication 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.

  5. Conditional statement - Wikipedia

    en.wikipedia.org/wiki/Conditional_statement

    A conditional statement may refer to: A conditional formula in logic and mathematics, which can be interpreted as: Material conditional; Strict conditional; Variably strict conditional; Relevance conditional; A conditional sentence in natural language, including: Indicative conditional; Counterfactual conditional; Biscuit conditional

  6. Necessity and sufficiency - Wikipedia

    en.wikipedia.org/wiki/Necessity_and_sufficiency

    Any conditional statement consists of at least one sufficient condition and at least one necessary condition. In data analytics , necessity and sufficiency can refer to different causal logics, [ 7 ] where necessary condition analysis and qualitative comparative analysis can be used as analytical techniques for examining necessity and ...

  7. Logical connective - Wikipedia

    en.wikipedia.org/wiki/Logical_connective

    I am indoors if and only if it is raining (). It is also common to consider the always true formula and the always false formula to be connective (in which case they are nullary ). True formula: ⊤ {\displaystyle \top } , 1 {\displaystyle 1} , V {\displaystyle V} (prefix), or T {\displaystyle \mathrm {T} } ;

  8. Vacuous truth - Wikipedia

    en.wikipedia.org/wiki/Vacuous_truth

    These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [11] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...

  9. Material conditional - Wikipedia

    en.wikipedia.org/wiki/Material_conditional

    The material conditional is also notated using the infixes and . [2] In the prefixed Polish notation , conditionals are notated as C p q {\displaystyle Cpq} . In a conditional formula p → q {\displaystyle p\to q} , the subformula p {\displaystyle p} is referred to as the antecedent and q {\displaystyle q} is termed the consequent of the ...

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