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2. Logical equivalence - Wikipedia

   en.wikipedia.org/wiki/Logical_equivalence

   In logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. [1] The logical equivalence of p {\displaystyle p} and q {\displaystyle q} is sometimes expressed as p ≡ q {\displaystyle p\equiv q} , p :: q {\displaystyle p::q} , E p q {\displaystyle {\textsf {E}}pq} , or p q ...

3. T-schema - Wikipedia

   en.wikipedia.org/wiki/T-schema

   For example, the sentence "'Snow is white' is true" becomes materially equivalent with the sentence "snow is white", i.e. 'snow is white' is true if and only if snow is white. Said again, a sentence of the form "A" is true if and only if A is true. The truth of more complex sentences is defined in terms of the components of the sentence:

4. Sentence (mathematical logic) - Wikipedia

   en.wikipedia.org/wiki/Sentence_(mathematical_logic)

   A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values : as the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.

5. Contraposition - Wikipedia

   en.wikipedia.org/wiki/Contraposition

   In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent inverted and flipped.

6. Glossary of logic - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_logic

   logically equivalent Referring to statements that have the same truth value in every possible scenario, indicating that they are interchangeable in logical reasoning. logicism The philosophical belief that mathematics can be reduced to logic and that all mathematical truths can be derived from logical axioms and definitions. Löwenheim–Skolem ...

7. Inverse (logic) - Wikipedia

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

   The inverse and the converse of a conditional are logically equivalent to each other, just as the conditional and its contrapositive are logically equivalent to each other. [1] But the inverse of a conditional cannot be inferred from the conditional itself (e.g., the conditional might be true while its inverse might be false [2]). For example ...