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In logic and related fields such as mathematics and philosophy, " if and only if " (often shortened as " iff ") is paraphrased by the biconditional, a logical connective [ 1 ] between statements. The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of ...
Logical consequence (also entailment) 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. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises.
List of paradoxes. Outline of public relations – Overview of and topical guide to public relations. Map–territory relation – Relationship between an object and a representation of that object (confusing map with territory, menu with meal) Mathematical fallacy – Certain type of mistaken proof.
The exception proves the rule is a phrase that arises from ignorance, though common to good writers. The original word was preuves, which did not mean proves but tests. [4] In this sense, the phrase does not mean that an exception demonstrates a rule to be true or to exist, but that it tests the rule, thereby proving its value.
Formal proof. In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (known as well-formed formulas when relating to formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence, according to the rule of inference. It differs from a natural language ...
This is a list of English words that are thought to be commonly misused. It is meant to include only words whose misuseis deprecated by most usage writers, editors, and professional grammarians defining the norms of Standard English. It is possible that some of the meanings marked non-standardmay pass into StandardEnglish in the future, but at ...
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. (Equivalently, it is impossible to have P without Q, or the ...
Common English usage misconceptions. Text from Robert Louis Stevenson 's Strange Case of Dr Jekyll and Mr Hyde featuring one-sentence paragraphs and sentences beginning with the conjunctions "but" and "and". This list comprises widespread modern beliefs about English language usage that are documented by a reliable source to be misconceptions.