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Syllogism is a deductive argument having two premises and a conclusion. The question

contains two premises statements and answer is to find the correct conclusion.

Types of Syllogism

1. All (Universal Positive - UP)

2. No (Universal Negative - UN)

3. Some (Particular Positive - PP)

4. Some Not (Particular Negative - PN)

Premise TypeSubject (A)

Distributed

Predicate (B)

Distributed

All A is BUniversal Positive

(UP)Yes No

No A is BUniversal Negative

(UN)Yes Yes

Some A is BParticular Positive

(PP)No No

Some A is Not

B

Particular Negative

(PN)No Yes

Subject & Predicate

In all the statements, first term (which is A) is called subject and second term (which is

B) is called predicate. Collectively, both can be referred to as objects or terms.

Classification of Statement

Every statement can be classified as one of UP, UN, PP and PN.

Standard Structure

For a two-statement syllogism question, there can be only three objects (or terms). The

question contains two premises statement. Your job is to find conclusion statement.

Each premise statement and conclusion statement conains two objects. One object is

common (Middle Term) in both the premises. Conclusion contains two objects which are

not common.

Premises: A --> B; B --> C (B is the middle term)

Conclusion: A --> C

Rules for Syllogism

1. When both the premises are negative or when both the premises are particular,

no conclusion can be derived.

2. The middle term must not appear in the conclusion. The middle term must be

distributed atleast once.

3. Term which is not distributed in the premise must not be distributed in the

conclusion.

4. When both premises are positive, conclusion will be positive.

5. If one of premises is particular, then conclusion is particular.

6. If one of premises is negative, then conclusion is negative.

Lets see how to find conclusion with the help of eamples.

Examples #1

Premises

All animals are mortal.

All men are animals.

First step is to classify the premise statements. Here statements are UP & UP. Check

Rule 1 and Rule 2 to confirm whether conclusion can be derived or not. In this case,

middle term (animals) is distributed in first statement, so conclusion can be derived.

Using Rule 4,5 & 6, you can say that conclusion will be Universal Positive (UP).

Conclusion: All men are mortal.

Example #2 (CAT 1999)

Given question has five statements followed by options containing three statements put

together in a specific order. Choose the option which indicates a valid argument, where

the third statement is a conclusion drawn from the preceding two statements.

Question statements

a. Apples are not sweet

b. Some apples are sweet

c. All sweets are tasty

d. Some apples are not tasty

e. No apple is tasty

Answer choices

1. cea

2. bdc

3. cbd

4. eac

You have to check answer choices one by one. Option 1 is correct.

A Logical Connective (also called a logical operator) is a symbol or a word which is

used to connect two or more sentences. Each logical connective can be expressed as a

truth function.

Logical connectives

1. NOT (Negation)

2. AND (Conjunction)

3. EITHER OR (Disjunction)

4. IF-THEN (Material Implication)

In logical reasoning, we deal with statements that are essentially sentences in English

language. However, factual correctness is not important. We are only interested in

logical truthfulness of the statements. We can represent simple statements using

symbols like p and q. When simple statements are combines using logical connectives,

compound statements are formed.

Negation - NOT

Negation is the opposite of a statement. For example,

Statement: It is raining.

Negation: It is NOT raining.

Disjunction - EITHER OR

When two statements are connected using OR, at least one of them is true. For

example,

Either p or q: p alone is true; q alone is true; both are true

In such situation, valid inference is If p did not happen, then q must happen. And If p did

not happen, then p must happen.

Conjunction - AND

When two statements are connected using AND, both statements have to be true for

compound statement to be true.

p and q: p should be true as well as q should be true

Material Implication - IF THEN

If p, then q (p --> q): It is read as p implies q. It means that if we know p has occured, we

can conclude that q has occured. In such situations, only valid inference is "If ~q, then

~p"; If q did not happen, then p did not happen.

Negation of Compound Statements

Negation (p OR q) is same as Negation p AND Negation q

Negation (p AND q) is same as Negation p OR Negation q 

Negation (p --> q) is same as Negation p --> Negation q

Logical Connectives Summary Table

Given Similar as Valid Inference

If p, Then q If ~q, Then ~p

Only If p, Then q If q, Then p If ~p, Then ~q

Unless p, Then q If ~p, Then q If ~q, Then p

Either p or q If ~p, Then q 

If ~q, Then p