Search results
Results From The WOW.Com Content Network
material conditional (material implication) implies, if P then Q, it is not the case that P and not Q propositional logic, Boolean algebra, Heyting algebra: is false when A is true and B is false but true otherwise. may mean the same as
Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).
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.
Perpendicularity of lines in geometry; Orthogonality in linear algebra; Independence of random variables in probability theory; Coprimality in number theory; The double tack up symbol (тлл, U+2AEB in Unicode [1]) is a binary relation symbol used to represent: Conditional independence of random variables in probability theory [2]
Since the converse of premise (1) is not valid, all that can be stated of the relationship of P and Q is that in the absence of Q, P does not occur, meaning that Q is the necessary condition for P. The rule of inference for necessary condition is modus tollens: Premise (1): If P, then Q; Premise (2): not Q; Conclusion: Therefore, not P
Material implication does not closely match the usage of conditional sentences in natural language. For example, even though material conditionals with false antecedents are vacuously true , the natural language statement "If 8 is odd, then 3 is prime" is typically judged false.
Logical equivalence is different from material equivalence. Formulas and are logically equivalent if and only if the statement of their material equivalence is a tautology.
Going from a statement to its converse is the fallacy of affirming the consequent.However, if the statement S and its converse are equivalent (i.e., P is true if and only if Q is also true), then affirming the consequent will be valid.