# Proposition

It consists of three parts:

- The subject.
- The predicate.
- The relation between the subject and the predicate is called â€˜copulaâ€™.

# Some Examples of Propositions

- All tigers are wild.
- No school boy is disciplined.
- Some girls are beautiful.
- Some pups are not cute.

A subject is that part of the proposition about which something is being said. A predicate, on the other hand, is that term of the proposition which tells something about the subject.
Thus, in the four propositions given above, tigers, school boy, girl and pups are subjects. The words wild, disciplined, beautiful and cute are predicates. The words â€˜areâ€™, â€˜isâ€™ and â€˜are notâ€™ are called copula.

# Types of Propositions

**Categorical proposition means the relationship between the subjective and predicative terms is categorical. In other words, the predicative terms affirm or deny the subjective term.**

*Categorical Proposition:*â€˜All S are P.â€™

â€˜No S are P.â€™

â€˜Some S are P.â€™

â€˜Some S are not P.â€™

**A hypothetical proposition is a type of conditional sentence in which the â€˜ifâ€™ clause is in present indefinite tense and the consequent clause in future tense.**

*Hypothetical Proposition:*If â€˜Sâ€™, then P.

**Disjunctive propositions are those in which there is an alternation between the first part and the second part of the statement.**

*Disjunctive Proposition:***Relational proposition may establish either blood relationship between subject and predicate or any other type of relationship. Mr. Jack is the father of Mr. John. We are establishing a relationship between the subjective and predicative terms. Similarly, if we say â€˜A is taller than Bâ€™ or â€˜A is as tall as Bâ€™, we are referring a particular type of relational proposition.**

*Relational Proposition:*# Types of Categorical Propositions

**A proposition where the subject either includes or excludes all is called universal proposition.**

*Universal Proposition:*Normally, universal proposition begins with â€˜allâ€™, â€˜everyâ€™, â€˜anyâ€™, etc., or â€˜noâ€™, â€˜none of theseâ€™, â€˜not a singleâ€™, etc.All girls are naughty.

No box is square shaped.

Universal proposition is again sub-divided into two categories.

If the subject of a categorical proposition refers to all for which it stands and if the proposition is affirmative, it is called universal affirmative proposition.*Universal Affirmative:*If the subject of a categorical proposition refers to all for which it stands and if the proposition is negative, it is called universal negative proposition.*Universal Negative:*

**If the subject does not refer to â€˜allâ€™, it is called particular proposition. The subject in this type of proposition can be â€˜someâ€™, â€˜almost allâ€™, â€˜manyâ€™, â€˜quite a fewâ€™, etc. Anything less than â€˜allâ€™ is considered as particular in logic.**

*Particular Proposition:*Particular proposition is again sub-divided into two categories.Some girls are naughty.

Some boxes are not square-shaped.

If the subject is not referring to â€˜allâ€™ and if the proposition is affirmative it is called particular affirmative proposition.*Particular Affirmative:*If the subject is not referring to â€˜allâ€™ and if the proposition is negative, it is called particular negative proposition.*Particular Negative:*

Type of Propositions |
Universal |
Particular |

Affirmative | â€˜Aâ€™ format All S are P |
â€˜Iâ€™ format Some S are P |

Negative | â€˜Eâ€™ format No S are P |
â€˜Oâ€™ format Some S are not P |

Classify the following propositions into their respective type of A, E, I or O.

1. | All watches are expensive. | [ ] |

2. | Some students are players. | [ ] |

3. | All frogs are amphibians. | [ ] |

4. | All mammals give milk. | [ ] |

5. | Some vegetables are green. | [ ] |

6. | Some fruits are not sweet. | [ ] |

7. | Many of the books are spoiled. | [ ] |

8. | Quite a few of the politicians are honest. | [ ] |

9. | Some toothbrushes are not soft. | [ ] |

10. | Children are generally honest. | [ ] |

# Confusing Categorical Propositions

Consider the statement, â€˜All students are not intelligentâ€™. This statement cannot be considered as universal negative proposition. In fact, it is an â€˜Oâ€™ proposition. The statement implies that â€˜Some students are intelligentâ€™ and â€˜some students are not intelligentâ€™. As the statement is negative, it is considered to be an â€˜Oâ€™ proposition.

# Exclusive Propositions

# Exceptive Propositions

â€˜All persons except one are bachelorsâ€™ is an â€˜Iâ€™ proposition and for reasoning purposes, it can be rewritten as â€˜Some persons are bachelors.â€™ But if exception is with a particular name, it will be considered a universal proposition.