# Syllogism

#### Chapter 23

5 Steps - 3 Clicks

# Syllogism

### Description

Syllogism is all about the questions which contain two or more statements and these statements are followed by two or more conclusions. Need to find out which of the conclusions logically follow from the given statements. The statements have to be taken true even if they seem to be at difference from the commonly known facts.
For such questions, need to take the help of Venn graphs. On the premise of the given statements, need to draw all the possible diagrams, and afterwards get the arrangement from each of these figures separately. Finally, the answer regular to the all the diagrams is taken.

### Concepts

Syllogism is a thing which signifies ‘type of thinking in which a conclusion is drawn from two statements’ i.e. deductive reasoning or syllogism is a mediate deductive gathering in which two propositions are given to the point that they together or all things considered recommend the third.
Hence, syllogism can be characterized as ‘a type of thinking in which the determination sets up a connection between two terms being identified with the same third term as inferred in the premises’.

Example:
1. All human beings are mortal.
2. The child is a human being.
3. The child is mortal.
Conclusion: Conclusion is reached through the medium of a middle term, i.e. ‘human being’, with both subject (children) and the predicate (mortal).
Therefore, in a syllogism two premises are necessary to arrive at a conclusion.

Proposition:
A proposition is the statement of a specific connection between two terms. The proposition comprises of three sections – two terms and the indication of connection between them:
(a) The subject.
(b) The predicate.
(c) The copula.
Subject: It is the term, about which something is expressed, i.e. insisted or denied.
Predicate: It which is stated about the subject, i.e. insisted or denied about the subject.
Copula: Denotes the relation between the subject and the predicate.

There are four types of propositions. They are:
1. Categorical proposition
2. Hypothetical proposition
3. Disjunctive proposition
4. Relational proposition
Out of all the types, only categorical proposition is discussed here.

Categorical proposition:
It makes a direct assertion.
It asserts something directly without any condition.
The predicate is either affirmed or denied unconditionally.

Example:
1. All the bats are balls.
2. Man is mortal.
3. Man is not a dog.
Conclusion:
The predicate ‘mortal’ is affirmed about the subject ‘man’ in the second proposition.
In the third proposition the predicate is denied.

Categorical proposition is broadly divided into two major forms. They are:
a) Universal categorical proposition
b) Particular categorical proposition

Universal categorical proposition
It will fully include or fully exclude the subject.
Example:
1. All politicians are liars.
It is represented by capital letter A.
Here, the including of members of a class is complete and hence universal.
2.No man is woman.
It is represented by capital letter E.
Here, one class is completely excluded from the second.

Particular categorical proposition
they either only partly include or only exclude the subject while making a statement.
hence, in this type the subjective term refers to less than all.
Example:
1. Some girls are beauitful.
It is denoted by capital letter I.
2. Some politicians are not liars.
It is denoted by capital letter O.

### Model Problems

Model 1: The question contains a statements followed by two conclusions numbered I and II. Consider the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Given:
a) If only conclusion I follows.
b) If only conclusion II follows.
c) If either conclusion I or II follows.
d) If neither conclusion I nor II follows.
e) If both conclusions I and II follows.
Statements:
All vegetables are plants.
No plant is flower.
Some flowers are jungles.
All jungles are trees.
Conclusions:
I: Some trees are plants.
II: no plant is tree.
Solution:

First and fourth are universal affirmative(A – type), Second statement is universal negative (E -type) and third statement is particular affirmative (I – type).
All vegetables are plants ⇒ No plant is flower.
A + E ⇒ E – type conclusion
Therefore, No vegetable is flower.
Now, No plant is flower ⇒ Some flowers are jungles.
E + I ⇒ $$O_{1}$$ – type conclusion
Therefore, Some jungles are not plants.
Now, Some flowers are jungles ⇒ All jungles are trees.
I + A ⇒ I – type conclusion
Therefore, Some flowers are trees.
Hence, Conclusion I and II form complementary pair.
Therefore, either I or II follows.

Model 2: The question contains a statements followed by two conclusions numbered I and II. Consider the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Given:
a) If only conclusion I follows.
b) If only conclusion II follows.
c) If either conclusion I or II follows.
d) If neither conclusion I nor II follows.
e) If both conclusions I and II follows.
Statements:
Some fruits are biscuits.
All biscuits are snacks.
Conclusions:
I: Some snacks are fruits
II: Some cakes are fruits.
Solution:

First and fourth premises are universal affirmative (A – type).
Second and third premises are particular affirmative (I – type).
Now, Some fruits are biscuits ⇒ All biscuits are snacks.
I + A ⇒ I – type conclusion.
Therefore, Some fruits are snacks.
Conclusion I is converse of this conclusion.
Therefore, only conclusion I follows.

Model 3: The question contains a statements followed by two conclusions numbered I and II. Consider the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Given:
a) None follows.
b) Only I and II follows.
c) Only II and III follows.
d) Only I and III follows.
e) All follows.
Statements:
All tables are boards.
All pens are boards.
All boards are papers.
Conclusions:
I: Some pens are tables.
II: Some papers are pens.
III: No pen is table.
Solution:

All the three premises are universal affirmative (A – type).
Now, All pens are boards ⇒ All boards are papers.
Hence, A + A ⇒ A – type conclusion.
Therefore, All pens are papers.
Conclusion II is converse to this conclusion.
Now, All tables are boards ⇒ All boards are papers.
Hence, All tables are papers.
Conclusions I and III form complementary pair.
Therefore, either conclusion I or III follows.

Model 4: The question contains a statements followed by two conclusions numbered I and II. Consider the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Given:
a) None follows.
b) Only I and II follows.
c) Only II and III follows.
d) Only I and III follows.
e) All follows.
Statements:
All jackets are trousers.
No trouser is shirt.
Some shirts are caps.
Conclusions:
Solution:

First premise is universal affirmative (A – type).
Second premise is universal negative (E – type).
Third is particular affirmative (I – type)
Now, All jackets are trousers ⇒ No trouser is shirt.
hence, A + E ⇒ E – type.
Conclusion is Sopme caps are not trousers.
Conclusion III is converse of the first.
Therefore, Only II and III follows.

Model 5: The question contains a statements followed by two conclusions numbered I and II. Consider the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Given:
a) None follows.
b) Only I and II follows.
c) Only II and III follows.
d) Only I and III follows.
e) All follows.
Statements:
Some tents are buildings.
Some buildings are chairs.
Some chairs are windows.
Conclusions:
I: Some windows are buildings
II: Some windows are tents.
III: Some chairs are tents.
Solution:

Given
Some windows are buildings, Some windows are tents and Some chairs are tents.
No conclusion follows from particular premises.
Hence, only conclusion I follows.