Syllogism is a form of reasoning in which the conclusion is drawn from two or three given propositions or statements. This implies that a conclusion is drawn from what is stated in the Major Premise and the Minor Premise. Generally, the sequence follows deductive reasoning, that is, the Major Premise comprises a general statement, moving to the particular in the Minor Premise, from which a conclusion is then drawn. For a syllogism to be valid, the conclusion must necessarily follow from the premises. For a syllogism to be true, it must make accurate claims and be consistent with facts. For a syllogism to be sound, it must be both true and valid.
How to tackle Syllogisms?
To tackle questions based on syllogism, the following points must be kept in mind:
1. Prepositions are of four types, namely:
- Universal Affirmative [the symbol to denote Universal Affirmative is (A)]
- Universal Negative [the symbol to denote Universal Negative is (E)]
- Particular Affirmative (the symbol to denote Particular Affirmative is (I)]
- Particular Negative [the symbol to denote Particular Negative is (O)]
Conclusions can be derived by applying the following rules:
a. It is not possible to get universal conclusion with two particular statements.
b. It is not possible to get negative conclusion with two affirmative sentences.
c. It is not possible to get positive conclusion with two negative statements.
d. It is not possible to get a conclusion with two particular statements. The exception to this rule is when a Particular Affirmative type of statement is given and by reversing it, a Particular Affirmative type of conclusion is given.
a. A Universal Negative statement when reversed, gives Universal Negative and Particular Negative as conclusion.
b. A Universal Affirmative statement when reversed, gives Particular Affirmative as conclusion.
c. A Particular Affirmative statement when reversed, gives Particular Affirmative as conclusion.
d. A Particular Negative statement when reversed, does not give a conclusion of any type.
Venn Diagrams and Syllogism
Venn Diagrams can be used to tackle Syllogism based questions.
Let’s consider some possibilities.
1. Some A's are B
- All A’s are B
- All B’s are A
- Some A are not B
- Some B are not A
2. All A's are B
- All A is B
- Some A is B
- Some B is A
- All B’s are A
- Some B’s are not A
3. No A is B
- No A is B
- No B is A
- Some A is not B
- Some B is not A
4. Some A's are not B
- Except All A’s are B, all other possibilities follow
Rules to keep in mind while using Venn Diagrams
- Draw the Venn diagram based on the statement given and the terms in the statement
- If the definite conclusion doesn’t satisfy the Venn diagram, then there is no need to check the possible conclusions
- If the definite conclusion does satisfy the Venn diagram, then it must satisfy all possible conclusions