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IMPLY can be denoted in algebraic expressions with the logic symbol right-facing arrow (→). Logically, it is equivalent to material implication, and the logical expression ¬A v B. There are two symbols for IMPLY gates: the traditional symbol and the IEEE symbol. For more information see Logic gate symbols.
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.
Suppose we are given that .Then we have by the law of excluded middle [clarification needed] (i.e. either must be true, or must not be true).. Subsequently, since , can be replaced by in the statement, and thus it follows that (i.e. either must be true, or must not be true).
The word "cause" (or "causation") has multiple meanings in English.In philosophical terminology, "cause" can refer to necessary, sufficient, or contributing causes. In examining correlation, "cause" is most often used to mean "one contributing cause" (but not necessarily the only contributing cause).
In formal languages, truth functions are represented by unambiguous symbols.This allows logical statements to not be understood in an ambiguous way. These symbols are called logical connectives, logical operators, propositional operators, or, in classical logic, truth-functional connectives.
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.
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction.
We can use the results about convergence of the sequence of partial sums of the infinite series and apply them to the convergence of the infinite series itself. The Cauchy Criterion test is one such application. For any real sequence , the above results on convergence imply that the infinite series