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In Disjunctive Syllogism, the first premise establishes two options. The second takes one away, so the conclusion states that the remaining one must be true. [3] It is shown below in logical form. Either A or B Not A Therefore B. When A and B are replaced with real life examples it looks like below.
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion is a necessary consequence of its premises. An argument that is not valid is said to be "invalid". An example of a valid (and sound) argument is given by the following well-known syllogism:
The central aspect of Aristotelian logic involves classifying all possible syllogisms into valid and invalid arguments according to how the propositions are formed. [112] [115] For example, the syllogism "all men are mortal; Socrates is a man; therefore Socrates is mortal" is valid. The syllogism "all cats are mortal; Socrates is mortal ...
A particular argument is valid if it follows a valid rule of inference. Deductive arguments that do not follow a valid rule of inference are called formal fallacies: the truth of their premises does not ensure the truth of their conclusion. [18] [14] In some cases, whether a rule of inference is valid depends on the logical system one is using.
A pure hypothetical syllogism is a syllogism in which both premises and the conclusion are all conditional statements. The antecedent of one premise must match the consequent of the other for the conditional to be valid. Consequently, conditionals contain remained antecedent as antecedent and remained consequent as consequent. If P, then Q.
Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q. Not Q. Therefore, not P." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument.
However, the logical validity of an argument is a function of its internal consistency, not the truth value of its premises. For example, consider this syllogism, which involves a false premise: If the streets are wet, it has rained recently. (premise) The streets are wet. (premise) Therefore it has rained recently. (conclusion)