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Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. [1] A sentence is said to be a logical consequence of a set of sentences, for a given language , if and only if , using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must ...
In propositional logic, material implication [1] [2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- P {\displaystyle P} or Q {\displaystyle Q} and that either form can replace the other in ...
It may be the case that several sufficient conditions, when taken together, constitute a single necessary condition (i.e., individually sufficient and jointly necessary), as illustrated in example 5. Example 1 "John is a king" implies that John is male. So knowing that John is a king is sufficient to knowing that he is a male. Example 2
13, then/if, Converse implication; 14, OR, Logical disjunction; 15, true, Tautology. Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples:
Every use of modus tollens can be converted to a use of modus ponens and one use of transposition to the premise which is a material implication. For example: If P, then Q. (premise – material implication) If not Q, then not P. (derived by transposition) Not Q. (premise) Therefore, not P. (derived by modus ponens)
This is more naturally stated as that the material nonimplication from to is true only if is true and is false. It may be written using logical notation as P ↛ Q {\displaystyle P\nrightarrow Q} , P ⊅ Q {\displaystyle P\not \supset Q} , or "L pq " (in Bocheński notation ), and is logically equivalent to ¬ ( P → Q ) {\displaystyle \neg (P ...
Answer: True – she does have a real name! 92. ... True or False Questions About History. 96. Coca-Cola was the first soft drink in the United States. Answer: False – it was Dr Pepper.
In this example there is no possible situation in which the premises are true while the conclusion is false. Since there is no counterexample, the argument is valid. But one could construct an argument in which the premises are inconsistent.