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Question digest :: you are looking for some guidance in the prepartion
and solvation
of Questions of type "inferences" which comes under syllogism. (those
mostly asked in civil exams)
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Definition(s)
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Inference : That which inferred; a truth or proposition drawn from
another which is admitted or supposed to be true; a
conclusion; a deduction. --Milton.
These inferences, or conclusions, are the effects of
reasoning, and the three propositions, taken all
together, are called syllogism, or argument. --I.
Watts.
Syn: Conclusion; deduction; consequence.
Usage: Inference, Conclusion. An inference is literally
that which is brought in; and hence, a deduction or
induction from premises, -- something which follows as
certainly or probably true. A conclusion is stronger
than an inference; it shuts us up to the result, and
terminates inquiry. We infer what is particular or
probable; we conclude what is certain. In a chain of
reasoning we have many inferences, which lead to the
ultimate conclusion. ``An inference is a proposition
which is perceived to be true, because of its
connection with some known fact.'' ``When something is
simply affirmed to be true, it is called a
proposition; after it has been found to be true by
several reasons or arguments, it is called a
conclusion.'' --I. Taylor.
Ref:- http://dict.die.net/inference
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Syllogism : The regular logical form of every argument, consisting of
three propositions, of which the first two are called the
premises, and the last, the conclusion. The conclusion
necessarily follows from the premises; so that, if these are
true, the conclusion must be true, and the argument amounts
to demonstration;
Note: as in the following example: Every virtue is laudable;
Kindness is a virtue; Therefore kindness is laudable.
These propositions are denominated respectively the
major premise, the minor premise, and the conclusion.
Note: If the premises are not true and the syllogism is
regular, the reasoning is valid, and the conclusion,
whether true or false, is correctly derived.
Ref:- http://dict.die.net/syllogism
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List of Rules of instances
~~~~~~~~~~~~
There are intotal a 9 valid argumentives inferences exits.The rules
of inferences are
listed below
1. Modus Ponens,
2. Modus Tollens,
3. Hypothetical Syllogism,
4. Disjunctive Syllogism,
5. Constructive Dilemma,
6. Absorption,
7. Simplification,
8. Conjunction, and
9. Addition.
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Basically Answers to these type of questions are determined by using a
Truth Table .
General form of a inference
premises 1
premises 2
'
'
'
premises n
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Conclusion
~~~~~~~~~~~~~~~~~~~~~~
Solvation methodology
~~~~~~~~~~~~~~~~~~~~~~
We can tabulate the truth-values of premises and conclusion,
checking for a line on which the premises are true while the conclusion is false.
Although this method always works, however, it isn't always convenient,
since the appropriate truth-table must have 2^n lines, where n is the number of
statement variables involved.
NOTE: for example if there are two statement variables... your truth
table will contain 2^2=4 lines...
so as statement variables incrases , truth table size increases ,
which takes much time in solving them
Explanation on each INFERENCE and how to solve each type?
1.Modus Ponens (latin : mode that affirms)is a valid ,simple argument
form .also abrivated as MP.
If P, then Q.
P.
Therefore, Q.
2.Modus Tollens (Latin: mode that denies) is the formal name for
indirect proof or proof by contrapositive, often abbreviated to MT
It is a common, simple argument form:
If P, then Q.
Q is false.
Therefore, P is false.
3.Hypothetical Syllogism : In logic, a hypothetical syllogism is a
valid argument of the following form:
P ? Q.
Q ? R.
Therefore, P ? R.
4. Disjunctive Syllogism :A disjunctive syllogism is one valid, simple
argument form:
A or B If not A Then B.
Here is an example:
Either I will choose soup or I will choose salad.
I will not choose soup.
Therefore, I will choose salad.
5.Constructive Dilemma : A logical constructive dilemma is a
formal logical argument that takes the form:
1 a) P ? Q.
b) R ? S.
2) Either P or R is true.
Therefore, either Q or S is true.
6.Absorption : A rule of inference of the form:
p superset of q
______________
p superset of ( p · q )
7. Simplification : In logic, simplification is a valid simple
argument of the form:
A and B, therefore A
or
A and B, therefore B
8.Conjunction :In logic and technical fields that use it, conjunction,
or and, is a logical operator in logical calculi, and a rule of
inference in deductive systems. The result of conjoining two
propositions is also called their conjunction. The conjunction is true
if both of the combined propositions are true; else it is false.
For two inputs A and B, the truth table of the operator is as follows.
A B A and B
F F F
F T F
T F F
T T T
9:Addition : A rule of inference of the form:
p
_____
p V q
Example: "It is raining. Therefore, either it is raining or the sun is shining."
for a detailed proof methods using truthtables please visit this page
:: philosophypages.com/lg/e11a.htm
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FREE Questions to practice
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http://www.dscs.state.la.us/Examining/SampleQuestions/inferences.htm
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Books for reference ::
you can find the related reference books under each topic in above reference url
thanks for giving me this opportunity,
-Niru
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