Monday, December 7, 2009

Deductive reasoning

It is a compulsory question in almost all entrance exams.

What type of question it contains :-

This type of question consists of two statements - on the basis of which we have to make deductions.

How many choices are there :-

The answer has to be chosen from 4-5 options that are available as choices.But , most importantly almost all questions of deduction consist of the option "none of the above" , which make the deduction a challenging task to solve in given time constraint.

How to approach:-

These can be approached by representing statements through venn diagrams.However there are also various simpler rules that must be taken care of before applying it in diagram( avoids unnecessary wastage of time).


What are premises and conclusion?

The statements given in the question are called premises.The answer obtained through deduction is called conclusion.

Starting word of premises(Quantifiers):

All->Every,Any,Each
No
Some->Many,Few,A little,Most of,More,Much of
Some-Not

Middle term:

The words that appear in both the premises is called middle term.

Types of premises :

  • Universal statements: All is used
  • Particular statements: Some is used
  • Negative premises: Not or No is used
  • Positive statements: Use of no or not is not there

Distribution Pattern:

Types of statements

Universal positive -> Subjects are distributed and predicate are not distributed
Universal negative -> Both subject and predicate are distributed
Distributed positive ->Both subject and predicate are not distributed
Distributed negative ->Subjects are not distributed and predicate are distributed

Rules for arriving at conclusion:

1)There should be only three distinct terms(not more not less).
2)If one premises is negative,conclusion is negative.
3)If one premises is particular,conclusion is also particular.
4)If both premises are negative or particular,no conclusion can be drawn.
5)No term can be distributed in conclusion,if it is not distributed in premises.

Examples to understand and apply the rules:

Example 1
1)All books are pages
2)All pages are boxes

Solution:
These are universally positive statements.The subject thus needs to be distributed and predicate is not distributed.Here, the middle term pages is distributed once on the premises.So , the conclusion is also universally positive.So,the solution will be:
All books are boxes

Example 2
1)All books are pages
2)All books are boxes

Solution:
These are universally positive statements.The subject thus needs to be distributed and predicate is not distributed.Here, the middle term books is distributed in both the premises.Thus the conclusion contain pages and boxes and both are not distributed which is possible in particular positive conclusion.So, the solution will be:
Some pages are boxes
Some boxes are pages

Example 3
1)All books are pages
2)All boxes are pages

Solution:
Here page is the middle term and is not distributed in any of the premises.Thus we cant derive any conclusions.


Example 4
1)All books are pages
2)Some books are boxes

Solution:
The first statement is universally positive statement and thus subject "book" is distributed and predicate "pages" is not distributed.The second statement is particular positive statement and thus both subject "book" and predicate "pages" are not distributed.Since, one conclusion is particular,solution is also particular.So, the solution will be:
Some pages are boxes
Some boxes are pages

Example 5
1)All books are pages
2)No pages are boxes

Solution:
The first statement is universally positive statement and thus subject "book" is distributed and predicate "pages" is not distributed.The second statement is universal negative statement and both subject "pages" and predicate "boxes" are distributed.The middle term "pages" in distributed in the second premises.As, one of the premises is negative,conclusion should be negative ad as both books and boxes are distributed,conclusion should be universally negative.
So, the solution will be:
No books are boxes
No boxes are books.

Example 6
1)All books are pages
2)Some pages are boxes

Solution:
The first statement is universally positive statement and thus subject "book" is distributed and predicate "pages" is not distributed.The second statement is particular positive where neither subject "pages" nor predicate "boxes" are distributed.As the middle term "pages" is not distributed at least once.So, no conclusion can be drawn.

Example 7
1)All books are pages
2)Some pages are not boxes

Solution:
The first statement is universally positive statement and thus subject "book" is distributed and predicate "pages" is not distributed.The second statement is particular negative statement and hence both subject "pages" and predicate "boxes" are not distributed.But, as middle term"pages" is not distributed at least once in premises.So, no conclusion can be drawn.

Example 8
1)All pages are books
2)Some pages are not boxes

Solution"
The first statement is universally positive statement and thus subject "pages" is distributed and predicate "books" is not distributed.The second statement is particular negative statement and hence both subject "pages" and predicate "boxes" are not distributed.As the middle man pages is distributed at least once and since one premises is particular and one premise is negative,so the conclusion will be "particular negative".So , the conclusion will be

Some books are not boxes.

Example 9
1)No books are pages
2)No pages are boxes

Solution:
Since both premises are universally negative,so no conclusion can be drawn.

Example 10
1)No books are pages
2)Some pages are not boxes

Solution:
Since both premises are negative,so no conclusion can be drawn.

Example 11
1)Some pages are not boxes
2)Some pages are books

Solution:

The first statement is particular negative statement and thus subject "pages" is not distributed and predicate "boxes" is distributed.The second statement is particular positive statement and hence both subject "pages" and predicate "books" are not distributed.Since middle man "pages" is not distributed in any of the premises , so no conclusion can be drawn.

Example 12
1)Some pages are not books
2)Some pages are not boxes

Solution:
Both the statement are particular negatives statement and thus subject "pages" is not distributed and predicate "books" is distributed in first statement and "pages" is not distributed and predicate "boxes" is distributed in second statement.As the middle man pages is not distributed at least once. So, no conclusion can be drawn.

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