FREE STUDY MATERIAL OF LOGICAL REASONING

FOR UGC NET PAPER 1

Overview of Arguments

An argument is a set of statements one of which (the conclusion) is taken to be supported by the remaining statements (the premises). [Note that a “statement” can either be a whole sentence, or an independent clause within a sentence.]

Three types of Arguments:

1. Deductive

2. Inductive, and

3. Abductive,

Deductive Argument: an argument where the conclusion follows validly from the premises. (In other words, an argument where the truth of the premises guarantees the truth of the conclusion)

Example:

Premises

All men are mortal

Socrates is a man

Conclusion Socrates is mortal

Inductive Argument:

An argument where the premises point several cases of some pattern and the conclusion states that this pattern will hold in general.

An inductive argument will not be deductively valid, because even if a pattern is found many times, that doesn’t guarantee it will always be found. Therefore, an inductive argument provides weaker, less trustworthy support for the conclusion than a deductive argument does.

Example:

Premises

We have seen 1000 swans. , and

All of them have been white.

Conclusion

All swans are white.

Abductive (or Hypothetico-Deductive) Argument:

An argument that (i) points out a certain fact, (ii) points out that if a certain hypothesis were true, we would get this fact, and so (iii) concludes that the hypothesis is indeed true.

Abductive arguments seem to make an even bigger jump than inductive arguments: inductive arguments generalize, while abductive arguments say that successful predictions prove the theory is true. Abductive arguments are not deductively valid, because false theories can make true predictions, so true predictions do not guarantee that the theory is true.

Example:

These coins conduct electricity (fact)

If these coins are made of gold (hypothesis),

then they would conduct electricity (prediction).

—————————————————————————————————

These coins are made of gold.

Venn diagram

A Venn diagram is an illustration of the relationships between and among sets, groups of objects that share something in common.

The main aim of this section is to test your ability about the relation between some items of a group by diagrams. In these questions, some figures of circles and some words are given. You have to choose a figure which represents the given words.

Representation of Some Conditions (Relations) is given below:

Condition 1:

If all the words are of different groups, then they will be shown by the diagram as given below. Dog, Cow, Horse

All these three are animals but of different groups, there is no relation between them. Hence they will be represented by three different 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 shown by the diagram as given below.

Unit, Tens, Hundreds

Ten units together make one Tens or in one tens, whole unit is available and ten tens together make one hundreds.

Condition 3:

If two different items are completely related to third item, they will be shown as below. Pen, Pencil, Stationery

Condition 4:

If there is some relation between two items and these two items are completely related to a third item they will be shown as given below.

Women, Sisters, Mothers

Some sisters may be mothers and vice-versa. Similarly, some mothers may not be sisters and vice-versa. But all the sisters and all the mothers belong to women group.

Condition 5:

Two items are related to a third item to some extent but not completely and the first two items totally different. Students, Boys, Girls

The boys and girls are different items while some boys may be students. Similarly, among girls some may be students.

Condition 6:

All the three items are related to one another but to some extent not completely. 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 items are related to each other completely and the third item is entirely different from first two. Lions, Carnivorous, Cows

All the lions are carnivorous but no cow is lion or carnivorous.

Condition 8:

The first item is completely related to the second and third item is partially related to the first and second item. Females, Mothers, Doctors

All Mothers belong to Females but some Mothers are Doctors but not all.

Condition 9:

The first item is partially related to second but third is entirely different from the first two. 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:

First item is completely related to second and third item is partially related to first and second item. Males, Fathers, Children

All Fathers belong to Male but Fathers are not Children.

SYLLOGISM

Deductive reasoning (logical) in which a conclusion is derived from two or more premises.

Eg :

Statements (Premises)

All Dogs are Cats ———-(1)

All Cats are Lions ————(2)

Conclusion :

All Dogs are Lions.

Premise – A premise consists of a subject and a predicate wherein the first term [eg. “Dogs” in statement (1)] is the subject and the second term [eg. “Cats” in statement (1)] the predicate.

Similarly, in statement (2) “Cats” is called the subject and “Lions” is called the predicate.

The word that occurs in both the premises is known as the “Middle Term”. (“Cat” in the example above). The premises can be divided into

Universal Statements (when “All” is used)
Particular Statements (when “Some” is used)

This classification of the premises into the above categories is dependent on the qualifier used in the premise.

For example, statements where “All” is used are called Universal statements and statements where “some” is used are called Particular Statements.

Simple Tricks to Solve Syllogism Questions Quickly:

Through the use of Venn Diagrams, you can solve syllogisms problems in an easy manner. Some Examples of Syllogisms solved using Venn Diagrams are:

(Example 1) Statements:

All Dogs are asses
2.All asses are bulls

Conclusions

1.Some dogs are not bulls. 2.Some bulls are dogs.

2.Some bulls are dogs.

3.All bulls are dogs. 4.All dogs are bulls.

4.All dogs are bulls.

Step 1: forget the solutions and concentrate on the Statements.

Step 2: On the basis of both statements, draw a Venn diagram:

From the diagram, it is clear that (2) and (4) conclusions logically flow.

(Example 2) Statements:

All the locks are keys.
2. All the keys are bats.
3. Some watches are

Conclusions:

Some bats are
Some watches are
All the keys are

Only (1) and (2)

Only (1)

Only (2)

Only (1) and (3)

From the Statements, there are 3 possible Venn Diagrams because there is no clarity about the Bats!

From the diagram, only option (2) only (1) logically satisfies all 3 statements.

RELATIONS OF IDENTITY AND OPPOSITION

Two ideas are identical or different accordingly as they have the same or a different content (the ideas of man and rational animal; of man and animal).

Opposition is an immediate inference grounded on the relation between propositions which have the same terms, but differ in quantity or in quality or in both.

In order that there should be any formal opposition between two propositions, it is necessary that their terms should be the same. There can be no opposition between two such propositions as these—

All angels have wings
No cows are carnivorous

If we are given a pair of terms, say A for subject and B for predicate, and allowed to affix such quantity and quality as we please, we can, of course, make up the four kinds of proposition recognized by logic, namely,

A. All Cats are Dogs

E. No Cats are Dogs

I. Some Cats are Dog

O. Some Cats are not Dogs

Now the problem of opposition is this: Given the truth or falsity of any one of the four propositions A, E, I, O, what can be ascertained with regard to the truth or falsity of the rest, the matter of them being supposed to be the same?

The relations to one another of these four propositions are usually exhibited in the following scheme—

(The square of opposition is a chart that was introduced within classical (categorical) logic to represent the logical relationships holding between certain propositions in virtue of their form. )

Contrary: Opposition is between two universals which differ in
Sub-contrary: Opposition is between two particulars which differ in
Subaltern: Opposition is between two propositions which differ only in
Contradictory: Opposition is between two propositions which differ both in quantity and in

Important Points

Contrary – A relation that holds only between the “A” (All Cats are Dogs) and “E” ( No Cats are Dogs) propositions, which say that, if one is true, the other must be false. Or, in other words, they cannot BOTH be true.

Subcontrary: A relation that holds only between the “I” (Some Cat are Dogs) and “O” (Some Cats are not Dogs) propositions, which say that, if one is false, the other must be true. Or, in other words, they cannot BOTH be false.

Tricks to solve questions of Square of Opposition –

If A be true ——– E is false —– O is false — I true

If A be false ——– E is unknown —— O true —— I unknown

If E be true ——– O is true ——– I false ———- A false

If E be false ——– O is unknown —— I true ——– A unknown

If O be true ——— I is unknown ——–A false —— A unknown

If O be false ——– I is true ———- A true ———- E false

If I be true ———- A is unknown ——- E false —— O unknown

If I be false ——— A is false ———- E True ——- O true

DEFINITIONS

A definition is a statement that gives the meaning of a term.

LEXICAL

The purpose of a lexical definition is to report the way a word is standardly used in a language. Most definitions found in a dictionary are lexical definitions.

Eg. Fossil, reptiles etc.

PERSUASIVE

The purpose of a persuasive definition is to influence people’s attitudes, not to neutrally and objectively capture the standard meaning of a word.

Eg. Teenagers, Abortion

STIPULATIVE

A stipulative definition stipulates (assigns) a meaning to a word by coining a new word or giving an old word a new meaning. A stipulative definition is neither true nor false; it is neither accurate nor inaccurate.

Eg. Sugarnecker, Black Holes, etc.

THEORITICAL

Theoretical definitions can explain concepts theoretically. Sometimes definitions are given for terms, not because the word itself is unfamiliar, but because the term is not understood. Such concepts require theoretical definitions, which are often scientific or philosophical in nature. For example, when your chemistry teacher defines water by its chemical formula H2O, he is not trying to increase your vocabulary (you already knew the term water), but to explain its atomic structure.

Accepting a theoretical definition is like accepting a theory about the term being defined. If you define spirit as “the life-giving principle of physical organisms,” you are inviting others to accept the idea that life is somehow a spiritual product.

PERSUASIVE

A precising definition takes a word that is normally vague and gives it a clear precisely defined meaning.

Eg. Lite, Low – income, middle aged, etc.

ANALOGY

Analogy means similarity. In this type of questions, two objects related in some way are given and the third object is also given with four or five alternatives. You have to find out which one of the alternatives bears the same relationship with the third objects as first and second objects are related.

Example 1:

Curd : Milk :: Shoe : ?

(A) Leather (B) Cloth

Answer: Option A

As curd is made from milk similarly shoe is made from leather.

Example 2:

Calf : Piglet :: Shed : ?

(A) Prison (B) Nest

Answer: Option C

Calf is young one of the cow and piglet is the young of Pig. Shed is the dwelling place of cow. Similarly Pigsty is the dwelling place of pig.

Example 3:

Malaria : Mosquito :: ? : ?

(A) Poison : Death (B) Cholera : Water

Answer: Option B

As malaria is caused due to mosquito similarly cholera is cause due to water.

Example 4:

ABC : ZYX :: CBA : ?

(A) XYZ (B) BCA

Answer: Option A

CBA is the reverse of ABC similarly XYZ is the reverse of ZYX.

Example 5:

4 : 18 :: 6 : ?

(A) 32 (B) 38

Answer: Option B

As, (4)² + 2 =18

Similarly, (6)² + 2 = 38.

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