Logical Reasoning

Introduction to logical reasoning

Logical Reasoning: The study of logic is also referred to as the study of reasoning. It is concerned with proposals and the elements that make them up. 

A proposition is a declarative sentence that states whether something is true or not. It may be broken down into four primary grammatical sections, just like any other sentence:

1. The subject term
2. The predicate term
3. The quantifier
4. The copula

Let's go over each term one by one.

   1. THE SUBJECT TERM: The subject of a proposition is the part of it about which anything is said. Consider the following scenario:



      2. THE PREDICATE TERM: The part of a phrase that tells us who or what the subject is. Consider the following scenario:




      3. THE QUANTIFIER: Quantifiers are words like "all," "no," and "some" that indicate an amount. Consider the following scenario:
 



 
     4. THE COPULA: A word or a group of words that link the proposition's subject and predicate. Consider the following scenario:




Let's have a look at the structure of a basic categorical proposition.
 

S.No.	Quantifier	Subject	Copula	Predicate
1	All	birds	can	fly
2	No	foxes	are	birds
3	Some	replies	are	snakes
4	All	S	are	P

NOTE: The letters 'S' and 'P' are used to denote the subject and predicate terms of a categorical proposition, respectively.

Quantity of categorical proposition :
The amount of a categorical proposition is a measurement of the degree to which the subject and predicate terms are related.

• If the asserted inclusion or exclusion holds for every member of the class represented by the subject term, the categorical proposition is a universal proposition. Take into account::

        1. All oranges are fruits.
        2. No dog can fly.

• If the asserted inclusion or exclusion holds for one or more members of the class defined by the subject term, a categorical proposition is a particular assertion. Consider the following scenario:

        1. Some animals are dogs.
        2. Some fruits are bitter.
Thus, the subject term is distributed in all propositions but undistributed in every particular proposition.

Quality of categorical proposition :
The nature of the link that a categorical proposition affirms between its subject and predicate terms is determined by its quality.

• Affirmative proposition: It states that the class designated by its subject term is included, either as a whole or only in part, within the class designated by its predicate term.
• Negative proposition: A categorical proposition is a negative proposition if it wholly or partially excludes members of the subject class from the predicate class. For example, No book is notebook

Let us understand this concept with few examples.

Examples 1:
For the following standard form categorical proposition, identify the subject, predicate, quantifier and copula.

1. Some dogs are wild animals.
2. Some teachers are terrible bores.
3. No coins are square object.
4. No teachers are students.

Solution : 

 

S.No.	Subject	Predicate	Quantifier	Copula
1	Dogs	Wild animals	some	are
2	teachers	terrible bores	some	are
3	coins	square object	No	are
4	teachers	students	No	are

Example 2: For the following standard form categorical proposition, identify the subject, predicate, quantifier and copula.

1. All lotus are flowers
2. Some animals can fly.
3. Every bird can fly.
4. No wheel barrows are comfortable.

Solution: 

 

S.No.	Subject	Predicate	Quantifier	Copula
1	lotus	flowers	All	are
2	animals	fly	some	can
3	bird	fly	every	can
4	wheel barrows	comfortable	No	are

  Logical Reasoning: The study of logic is also referred to as the study of reasoning. It is concerned with proposals and the elements that make them up. 

A proposition is a declarative sentence that states whether something is true or not. It may be broken down into four primary grammatical sections, just like any other sentence:

1. The subject term
2. The predicate term
3. The quantifier
4. The copula

Let's go over each term one by one.

   1. THE SUBJECT TERM: The subject of a proposition is the part of it about which anything is said. Consider the following scenario:



      2. THE PREDICATE TERM: The part of a phrase that tells us who or what the subj…