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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.
Logical consequence (also entailment or implication) is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
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 ...
Grammatically, one cannot infer "all mortals are men" from "All men are mortal". An type "A" proposition can only be immediately inferred by conversion when both the subject and predicate are distributed, as in the inference "All bachelors are unmarried men" from "All unmarried men are bachelors".
A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules.
If P and Q are "equivalent" statements, i.e. , it is possible to infer P under the condition Q. For example, the statements "It is August 13, so it is my birthday" P → Q {\displaystyle P\to Q} and "It is my birthday, so it is August 13" Q → P {\displaystyle Q\to P} are equivalent and both true consequences of the statement "August 13 is my ...
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle (300s BCE).
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.