Quick Revision on Syllogism

Quick Revision on Syllogism : Hello friends,here we are providing you with syllogism basics and all the expected cases with the conclusions . Hope it helps you all to clear the concepts of syllogism.

Enjoy Reading !!!!!!!!!!!!!!!!!

Quick Revision on Syllogism

“Premises” – Statements given in the question
“Conclusion” – answer, that follows

All P are Q
All Q are R
The above two statements are called “Premises”.

Conclusion :
All P are R.

The premises normally start with – All,No,Some,Many,Some,Not – they are called qualifiers.

Premise has two parts subject and predicate
First term “P” is the subject
Second term “Q” is thepredicate.

The word that occurs in both the premises is known as the “Middle Term”. (eg:”Q”).
The “Conclusion” should consist of the other two words (P and R)the middle term should not appear in the answer.

The premises can be divided into

• Universal Statements
• Particular Statements

Where “All” is used are called Universal statements
Statements where “Some” is used are called Particular Statements.

Premises can also be divided into

• Positive (affirmative) statements and
• Negative statements

When Negative term like “not” or “no” is there in the statement, it is called a negative premise.
Otherwise it is called a positive premise or an affirmative statement.

Important Rules for Syllogism:

1. Every deduction should contain three and only three terms.
2. The middle term must be distributed at least once in the premises.
3. If one premise is negative the conclusion must be negative.
4. If one premise is particular the conclusion must be particular.
5. If both premises are negative no conclusion can be drawn.
6. If both premises are particular no conclusion can be drawn.
7. No term can be distributed in the conclusion if it is not distributed in the premises.

Examples containing all the cases:

Example 1 :

• All P are Q
• All Q are R

Ans:All P are R

Example II :

• All Q are P
• All Q are R

Ans: “Some P are R” or “Some R are P”

Example III :

• All P are Q
• All R are Q

Ans: we cannot draw any conclusion in this case.

Example IV :

• All Q are P
• Some Q are R

Ans:Some P are R or Some R are P

Example V :

• All P are Q
• No Q are R

Ans: No P are R or No R are P

Example VI :

• All P are Q
• Some Q are not R

Ans: No conclusion can be drawn

Example VII :

• All Q are P
• Some Q are not R

Ans: Some P are not R

Example VIII:

• No P are Q
• No Q are R

Ans: No conclusion can be drawn

Example IX :

• No P are Q
• Some Q are not R

Ans: No conclusion can be drawn

Example X :

• Some Q are not R
• Some Q are P

Ans: No conclusion can be drawn

Example XI :

• Some Q are not P
• Some Q are not R

Ans: No conclusion can be drawn