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  2. Logical equivalence - Wikipedia

    en.wikipedia.org/wiki/Logical_equivalence

    Formulas and are logically equivalent if and only if the statement of their material equivalence is a tautology. [ 2 ] The material equivalence of p {\displaystyle p} and q {\displaystyle q} (often written as pq {\displaystyle p\leftrightarrow q} ) is itself another statement in the same object language as p {\displaystyle p} and q ...

  3. Tautology (logic) - Wikipedia

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

    A tautology in first-order logic is a sentence that can be obtained by taking a tautology of propositional logic and uniformly replacing each propositional variable by a first-order formula (one formula per propositional variable).

  4. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.

  5. Truth table - Wikipedia

    en.wikipedia.org/wiki/Truth_table

    Inspection of the tabular derivations for NAND and NOR, under each assignment of logical values to the functional arguments p and q, produces the identical patterns of functional values for ¬(p q) as for (¬p) q), and for ¬(p q) as for (¬p) q). Thus the first and second expressions in each pair are logically equivalent ...

  6. List of rules of inference - Wikipedia

    en.wikipedia.org/wiki/List_of_rules_of_inference

    With this premise, we also conclude that q=T, p∨q=T, etc. as shown by columns 9–15. 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.

  7. Propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Propositional_calculus

    Some of these connectives may be defined in terms of others: for instance, implication, p q, may be defined in terms of disjunction and negation, as ¬p q; [74] and disjunction may be defined in terms of negation and conjunction, as ¬(¬p ¬q). [51]

  8. Law of excluded middle - Wikipedia

    en.wikipedia.org/wiki/Law_of_excluded_middle

    The proof of 2.1 is roughly as follows: "primitive idea" 1.08 defines p q = ~p q. Substituting p for q in this rule yields p p = ~p p. Since p p is true (this is Theorem 2.08, which is proved separately), then ~p p must be true. 2.11 p ~p (Permutation of the assertions is allowed by axiom 1.4)

  9. Logical connective - Wikipedia

    en.wikipedia.org/wiki/Logical_connective

    Of its five connectives, {, , , ¬, ⊥}, only negation "¬" can be reduced to other connectives (see False (logic) § False, negation and contradiction for more). Neither conjunction, disjunction, nor material conditional has an equivalent form constructed from the other four logical connectives.