Deductions

This is a part of Logical ability section, we are supposed to draw conclusions using given existing data but not from our usual life it's something life nature v/s nurture where we have to consider nurture but not generic nature, you will understand this by the end.
Example
All girls are women.
Some women are pregnants.
the conclusion can be: some girls are pregnants.(-or- some girls are not pregnants)

Deduction:
A form of reasoning with 2 premises and 3 terms.

Middle term:
A term which is common in both the given premises.
Distribution of a term:
A term is said to be fully distributed if all of it or none of it is considered in the premise.

classification:

1. Universal premise: Premise which includes the full portion of an item.

• (i)All A is B. (+ve premise)
• (ii)No A is B.(-ve premise)

2. Particular premise: Premise which does not include the full portion of an item.

• (iii)Some A is B. (+ve premise)
• (iv)Some A is not B.(-ve premise)

If a sentence has "all" or "not" as prepositions, that sentence is fully distributed.

If a sentence has "some" as a preposition, that is non-full distribution.
A premise with "not" is considered as a negative premise.

From the above four sentences, we can find the distribution of items as follows.

Statement            A's Distribution            B's Distribution
(i)                        Fully         (F)               Not Fully (NF)
(ii)                       Fully         (F)               Fully        (F)
(iii)                      Not Fully (NF)             Not Fully (NF)
(iv)                      Not Fully (NF)             Fully        (F)

Weakness: A premise is said to be weak if it is -ve premise or Not fully distributed or both.


Logical Deduction rules:

• Premises must have only 3 terms.
• A conclusion absorbs all the weakness of premises.
• There should be a middle term in common for both the statement.
• The middle term should be fully distributed at least once in premises.(if not, proper conclusion cannot be drawn)
• The term which is undistributed in premises remains undistributed in conclusion.
• Term which is fully distributed in premise can be either distributed or Not distributed.

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Example1:

All rupees are notes.

All notes are papers.

solution:

All (F) rupees are (NF) notes.  {notes is middle term, (F) at least once.}

All (F) notes are (NF) papers.

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All (F) rupees are (NF) papers.      [or] some rupees are papers. [or] some papers are rupees.

Example2:
Some countries are islands.
No islands are drought prone.
solution:
Some(F) countries are (NF) islands.   {Middle term: Islands,(F) once}
No (F)islands are (NF) drought prone.

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some + not                      {All weakness}

Some countries are not drought prone.

Example3:

All boys are humans.

No human is kind.

solution:

All (F) boys are (NF) humans.        {Middle term: Humans}

Some (NF) humans are (NF) bad.

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No proper conclusion can be drawn {Middle term is (NF) in both premises.}

Example4:

Some (NF) Boys are (NF) Pregnants.   {Middle term: pregnants, (F) once}

All (F) pregnants give birth to a (NF) child.

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Some                                           {weakness}

Some Boys give birth to a child.

Note: while deducting conclusions, you need not consider the original meaning.