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  2. 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 ...

  3. 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 ...

  4. Conditional sentence - Wikipedia

    en.wikipedia.org/wiki/Conditional_sentence

    A conditional sentence expressing an implication (also called a factual conditional sentence) essentially states that if one fact holds, then so does another. (If the sentence is not a declarative sentence, then the consequence may be expressed as an order or a question rather than a statement.)

  5. List of rules of inference - Wikipedia

    en.wikipedia.org/wiki/List_of_rules_of_inference

    The column-11 operator (IF/THEN), shows Modus ponens rule: when p→q=T and p=T only one line of the truth table (the first) satisfies these two conditions. On this line, q is also true. Therefore, whenever p → q is true and p is true, q must also be true.

  6. Necessity and sufficiency - Wikipedia

    en.wikipedia.org/wiki/Necessity_and_sufficiency

    In mathematics, theorems are often stated in the form "P is true if and only if Q is true". Because, as explained in previous section, necessity of one for the other is equivalent to sufficiency of the other for the first one, e.g. P ⇐ Q {\displaystyle P\Leftarrow Q} is equivalent to Q ⇒ P {\displaystyle Q\Rightarrow P} , if P is necessary ...

  7. 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

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