UGC NET Notes on Logical Reasoning (Part-II)
1. Relations of Identity and Opposition
In Relations of Identity and Opposition, we will study the relations among the propositions.
- These propositions are formed when a subject and predicate are given.
Suppose we are given A as a subject and B as a predicate. Then, we can generally make the following four propositions with both these subject and predicate.
A. All A’s are B’s –Universal Positive
B. No A’s are B’s - Universal Negative
C. Some A’s are B’s are - Particular Positive
D. Some A’s are not B’s - Particular Negative
Square of Opposition: AEIO Rule of Syllogism
Now, to identify the relation among these propositions, we will have to understand the square of opposition chart.
This subpart is very important from the point of view of examination.
- The relations of the given four propositions-A,E,I,O amongst one another are usually depicted in the following scheme— Square of opposition.
- It is a chart that was introduced within classical logic to represent the logical relationships existing between the various propositions
Following relations are made among the propositions:
- Sub Altern
- Sub Contraries
Let us understand in detail:
Contradictory statements are A and O, E and I
- A and O Both cannot be true or false together means if one is false then other must be true.
- If A is true then O is false or If O is true then A is false
- Similarly, E and I cannot be true or false together means if one is false then other must be true.
Contrary statements are A and E
- BothA and E cannot be true together but can be false together.
3. Sub Altern:
Sub Altern statements are A and I, E and O
- These statements are truth Downward but False Upward
- If A is true then I is true and If I is true then A is false
- If E is true then O is true and If O is true then E is false
4. Sub Contraries:
Sub Contrary Statements are I and O.
- These statements can be claimed to be true together but cannot be false together.
Following type of question is generally asked in the exam:
For eg: If the statement ‘All Men wins the race’ is false which of the following statements can be considered to be true?
Select the correct choice :
- All Men win the race.
- Some persons who win the race are not men
- Some persons who win the race are men.
- No person who wins the race is men
All men wins the race is false, it is an A statement, according to contradictories, A and O are opposite. Therefore, the correct answer is B - Some persons who win the race are not men.
An argument is a series of statements, called the premises, intended to determine the degree of truth of another statement, the conclusion.
All musician can read music
Ram is a musician
Ram can read music.
Types of Arguments
There are generally two types of arguments as follows:
- Deductive Argument/Deductive Reasoning
- Inductive Argument/ Inductive Reasoning
- Abductive (or Hypothetico-Deductive) Argument/ Abductive Reasoning
1. Deductive Argument:
- Deductive argument starts out with a general statement and examines the possibilities to reach a specific, logical conclusion..
- It is considered as from general to particular.
- In this, the premises are intended to provide support for the conclusion that is so strong that, if the premises are true, it would be impossible for the conclusion to be false.
All dogs have long ears
Tuffy is a dog
Therefore, Tuffy has long ears.
2. Inductive Argument:
- It refers to an argument that takes specific information and makes a broader generalisation that is considered probable, allowing for the fact that the conclusion may not be accurate.
- It observes some common pattern among the premises and conclusion and that observed pattern will hold in general according to this argument.
- Inductive arguments make generalisation.
- It is considered as from particular to general.
We have seen several Americans
All of them have fair complexion
All Americans have fair complexion
3. Abductive (or Hypothetico-Deductive) Argument:
- Abductive argument is to take away a logical assumption, inference, conclusion, hypothesis, or best guess from an observation or set of observations.
- The conclusion drawn is just a best guess, it may or may not be true.
A person enters into his room and finds torn up papers lying all over the floor.
He realises that dog has been alone in the room all day.
The person draws a conclusion that the dog tore up the papers
Analogy is a type of reasoning in which a comparison is made between things that have similar features, Or in other words, analogy means similarity.
1. Tree: Leaf:: Flower : Petal
2. Hammer: Nail :: Comb : Hair
How to solve Analogy questions?
In this type of questions, given two objects are related in some or the other way and the third object is also given with four or five options. You have to figure out which one of the options has the same relationship with the third objects as first and second objects has.
Shimla : Himachal Pradesh :: Jaipur : ?
As Shimla is state capital of Himachal Pradesh In the same way Jaipur is the capital of Rajasthan.
Bones : Orthopaedic :: Skin : ?
As Orthopaedic is a specialist doctor for bones, similarly Dermatologist is a specialist doctor for skin diseases.
ABCD : ZYXW :: DCBA : ?
As DCBA is the reverse of ABCD, in the same way WXYZ is the reverse of ZYXW..
10 : 99 :: 5 : ?
As, (10)2 -1 = 100-1=99. In the same way, (5)2-1=24. The correct answer is B.
All the best for your exams,
Team BYJU'S Exam Prep