UGC NET: Logical Reasoning Notes
In these notes, we will discuss Venn Diagrams and Syllogism.
1. Venn Diagram: A Venn diagram refers to an illustration of the relationships between and among sets or groups of objects that share something in common.
- The main objective of this section is to test your ability to the relation between some words of a group by diagrams.
- In these questions, you will be some figures of circles and some in words. You have to choose a figure which represents the given words to the maximum extent.
- Representation of some conditions (relations) has been shared below:
Condition 1: If all the words belong to different groups, then they will be shown by the diagram as given below.
Example: Rat, Cow, Horse
All the mentioned words are animals but belong to different groups, therefore, there is no relation among them. Hence they will be represented by three separate circles.
Condition 2: If the first word is related to the second word and the second word is related to the third word, then they will be depicted by the diagram as given below.
Example: Unit, Tens, Hundreds
Ten units together make one Ten or in one ten, the whole unit is available and ten tens together make one hundred.
Condition 3: If two altogether different words are completely related to the third word, they will be shown below.
Example: Eraser, Pencil, Stationery
Condition 4: If there is some relation between two words and these two words are completely related to a third word they will be shown as given below.
Example: Women, Sisters, Mothers
Some sisters may be mothers and vice-versa. Similarly, It is possible that some mothers may not be sisters and vice-versa. But all the mothers and all the sisters belong to the women group.
Condition 5: If two words are related to a third word to some extent but not completely and the first two words totally different.
Example: Students, Boys, Girls
The boys and girls are entirely different words while some boys may be students. Similarly, among girls, some may be students.
Condition 6: All the three words are related to one another but to some extent not completely.
Example: Boys, Students, Athletes
Some boys may be students and vice-versa. Similarly, some boys may be athletes and vice-versa. Some students may be athletes and vice-versa.
Condition 7: Two words are related to each other completely and the third word is entirely different from the first two.
Example: Lions, Carnivorous, Cows
All the lions belong to the carnivorous category but no cow is a lion or carnivorous.
Condition 8: The first word is completely related to the second and third word is partially related to the first and second word.
Example: Females, Mothers, Doctors
All Mothers belong to Females category but some Mothers are Doctors but not all.
Condition 9: The first word is partially related to second but third is entirely different from the first two.
Example: Dogs, Flesh-eaters, Cows
Some dogs are flesh-eaters but not all while any dog or any flesh-eater cannot be a cow.
Condition 10: The first word is completely related to the second and third word is partially related to the first and second word.
Example: Males, Fathers, Children
All Fathers belong to the Male category but Fathers are not Children.
2. Syllogism: Syllogism refers to a logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions (premises) that are asserted or assumed to be true.
(a). Statements (Premises): All Dogs are Rats ——(1)
All Rats are Lions ——(2)
(b). Conclusion: All Dogs are Lions.
(c). Premise: A premise consists of two parts mainly: Subject and a Predicate.
- In the first statement- Dogs is the subject and the Rats is the predicate.
- Similarly, in second statement “Rats” is called the subject and “Lions” is called the predicate.
- The word that occurs in both the premises i.e. common in both statements is known as the “Middle Term”. For eg: “Rats” is the middle term in the example above.
The premises can be divided into two four categories:
- Universal Statements (where “All” is used): All A’s are B’s.
- Particular Statements (where “Some” is used): Some A’s are B’s
- Universal Negative Statements. (where “No” is used): No A is B.
- Particular Negative Statements (where “Some not” is used): Some A’s are not B’s
This classification of the premises into the above-mentioned categories is dependent on the qualifier used in the premise.
Easy Trick to Solve Syllogism Questions Quickly
Syllogisms problems can be solved in an easy and quick manner through the use of Venn Diagrams. The examples of Syllogism solved using Venn Diagrams have been provided below.
- All Dogs are cats.
- All Cats are bulls.
- Some bulls are dogs.
- Some dogs are no bulls
- All dogs are bulls.
- All bulls are dogs.
Steps to solve the question:
Step 1: Forget the solutions and pay attention to the Statements.
Step 2: On the basis of the given statements, draw a Venn diagram as follows:
From the diagram, it can be stated that (1) and (3) conclusions logically flow.
- Most CPUs are keyboards.
- No keyboard is a Mouse.
- All Mouses are CPU.
- Some keyboards are CPU
- All CPU is Mouse
- No Mouse is a keyboard
- Some Mouse is a keyboard
(A) Only I follows
(B) Only II and III follow
(C) Only I and III follow
(D) Only II follows
From the diagram, it is clear that Conclusions I and III follow logically.
You can practice more questions of a similar type for a better understanding.
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