Logical Deduction

The phenomenon of deriving a conclusion from a single proposition or a set of given propositions, is known as logical deduction. The given proposition are also referred to as the premises.

There are two inferential processes of deduction:

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I. Immediate Deductive Inference

Here conclusion is deduced from one of the given propositions, by any of the three ways – Conversion, Obversion and Contraposition.

(1) Conversion:

In this inference, the subject term and the predicate term is interchanged i.e the Subject term of the premise becomes the predicate term of the conclusion and the predicate term of the premise become the Subject term of the conclusion.

The given proposition is called convertend and the conclusion drawn from it is called converse.

Table of Valid Conversions:

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Note: in a conversion the quality remains the same and the quantity may change.

(2) Obversion

In obversion, we change the quality of the proposition and replace the predicate terms by its complement.

The given proposition is called Obvertend and the conclusion drawn from it is called Obverse.

Table of Valid Obversions:

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(3) Contrapositions

To obtain the contrapositive of a statement, we first replace the subject and predicate terms in the proposition  and then exchange both these terms with their complements. Relatively simpler one!

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Note: The valid converse, obverse or contrapositive of a given proposition always logically follows from the proposition.

II. Mediate Deductive Inference (Syllogism)

First introduced by Aristotle, a Syllogism is a deductive argument in which conclusion has to be drawn from two propositions referred to as the premises.

Complete details of which is given in the next post.Click Here

An important point to remember:

While deriving logical conclusions, always remember that the following conclusions hold:

  1. The converse of each of the given premises
  2. The conclusions that directly follows from the given premises in accordance with the rules of syllogism
  3. The converse of the derived conclusions.

 

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