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Prototypical conditional sentences in English are those of the form "If X, then Y". The clause X is referred to as the antecedent (or protasis), while the clause Y is called the consequent (or apodosis). A conditional is understood as expressing its consequent under the temporary hypothetical assumption of its antecedent.
A conditional sentence is a sentence in a natural language that expresses that one thing is contingent on another, e.g., "If it rains, the picnic will be cancelled." They are so called because the impact of the sentence’s main clause is conditional on a subordinate clause.
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [ 1 ] and the LaTeX symbol.
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 ...
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
In logic and mathematics, the transitive closure of a relation, capturing the idea of indirect relationships across generations or iterations. antecedent The first part of a conditional statement, the "if" clause, which specifies a condition for the consequent. anti-extension
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P.
Causal conditional, if X then Y, where X is a cause of Y; Conditional probability, the probability of an event A given that another event B; Conditional proof, in logic: a proof that asserts a conditional, and proves that the antecedent leads to the consequent; Material conditional, in propositional calculus, or logical calculus in mathematics ...
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