As we see earlier deductive form of logical inference can be divided to immediate and mediate inference. In mediate inference the conclusion follows from more than one proposition. Syllogism is the form of mediate inference in which there are only two premises and the conclusion follows from them jointly.
Example:
1. All men are mortal.
2. All kings are men.
Therefore all kings are mortal.

1. All men are good.
2. Rama is a man.
Therefore Rama is good.

In the above example, the first two statements or the propositions are termed as 'Premises'. The first proposition or the first premise i.e. 'All men are mortal' is formed as 'major premise'. Whereas the second proposition i.e. 'All kings are men' is termed is 'minor premise'. Both the statements taken together are called 'Premises', 'Men', 'Mortal', and 'Kings' are called the terms of Syllogism. Evidently there are three terms in the premises i.e. 'Men', 'Mortal' and 'Kings', though the term men exists in the major premise as well as in the minor premise. The term which is common in both the premises i.e. 'The connecting term' is called the Middle term. In the above example me term men is middle term.

Types of Syllogism

There are five types of Syllogisms:

1. Categorical Syllogism: In this syllogism all the propositions are Categorical:
Statement: All men eat food.
All graduates are men.
Conclusion: All graduates eat food.

2. Hypothetical-Categorical Syllogism
In this the major premise is hypothetical and the other is categorical.
Statement: If graduates get jobs, they get food to eat.
All graduates get job.
Conclusion: All graduates get food to eat.

3. Disjunctive-Categorical Syllogism
In this major proposition is disjunctive, while the other is categorical.
Statement : Either a man is a saint or a sinner.
Everybody is a sinner.
Conclusion: Everybody is a sinner.
4. Relational Syllogism
In this type of syllogism the relational proposition brings us to a conclusion.
For example:
Statement : Tata is richer than Birla.
Birla is richer than Ambani
Conclusion : Tata is richer than Ambani. (Never think about the real situation)
5. Syllogism of Dilemma
In syllogism of dilemma major proposition is a double hypothetical and the minor is a disjunctive. This carries us to a disjunctive or categorical inference.

Principle of Syllogism

1. A syllogism is not dogmatic. It is based on reasonable propositions. The conclusion is derived according to the laws of logic.
2. A syllogism justifies its conclusion by showing the reasonability of the premises on which it is founded.
3. If a syllogism is not based on reason, it flounders. It appeals to reason and compels judgment.
4. It is important that the premises must be taken for granted. If the premises themselves are under dispute, then the entire superstructure of the edifice falls down like a house of cards.
5. The assumption of syllogistic reasoning is that the premises are acceptable universally or at any rate by the majority of me thinkers.
6. There is an interdependence of propositions in the syllogistic reasoning.
7. The categorical syllogism in a process of comparison :
Statement : All Indians are religious.
Mahathma Gandhi is an Indian

Conclusion: Mahathma Gandhi is religious.

In categorical syllogism the following rules are to be considered.
1. Every syllogism must contain three terms.
2. The middle term must be distributed at least once in the premise
3. If one premise is negative, the conclusion is negative.
4. If the premises are two negative propositions, no conclusion can be drawn.
5. If both premises are affirmative, the conclusion is affirmative.
6. If both premises are particular, no conclusion will be drawn.
7. From a particular major premise and a negative minor premise, no conclusion can be drawn.
8. If one premise is particular, the conclusion is particular.
9. No term can be distributed in the conclusion if it is not distributed in the premises.


Fallacies:

Fallacies literally mean misleading arguments. In logic there are certain rules. Violations of those rules leads to fallacious conclusions and hence the conclusion arrived at will be invalid.
1. Undistributed middle: (violation of rule 2above)
Eg: All fruits are good for men.
Bread is good for men.
Therefore bread is a fruit. The middle term "good for men" is undistributed and therefore, the conclusion is fallacious.
2. Fallacies of Diction: Here the use of ambiguous words in statements amounts to a fallacy.
Eg: Fruits are good.
Good is the aim of our life.
Therefore, the aim of our life is fruits.
Here the middle term 'good' is used in different senses
3. Fallacy of two negative premises :(Violation of rule 4 above)
Eg: No quadrupeds are rational
No Indians are quadrupeds.
Therefore no Indians are rational. The conclusion is invalid
4. Fallacy of two particular premises (violating of rule 6. above)
Eg: Some men are good.
Some men are honest.
Therefore some honest being are good. The conclusion is invalid
5. Illicit process: When the term undistributed in its own premise is distributed in the conclusion, an illicit fallacy occurs.
Eg: Some intelligent persons are liars
Rama is a liar.
Therefore Ram is intelligent.
6. Fallacy of amphibology: When the construction of the sentence is misleading, it results into fallacy.
Eg: "Ram, Krishna will go".
In this statement it is not clear as to who will go.
7. Fallacies of composition and division: When certain things are taken separately, it is true but when they are taken collectively it leads to fallacious conclusion.

Eg: Three and two are odd and even.
Three and two are five.
Hence, five is odd and even.

ASSUMPTIONS

In these questions one statement is followed by two other statements. The latter statements are said to be assumptions.
Assumption means anything that we assume to be true of a statement. For example if I say " we lost the match to Australia," I am assuming that 'we played a match with Australia,' If this is not the assumption my statement is wrong.

FORCEFULNESS OF ARGUMENT

In this type, a problem is posed in an interrogative sentence followed by two arguments. Generally one of which is affirmative and begins with 'Yes' and the other is negative with "No' .The strong arguments must be both important and directly related to the question. Weak arguments may be indirectly selected to the question and may be of minor importance. To determine the forcefulness of argument, the following rules are to be considered.
(a)The argument should be factual-based on, facts and not an assumption.

(b)The argument should be specific and not genera¬ised.

(c)The argument should be in conformity with the prevailing ideas and truth and should support the current thinking of the majority.

(d)There should not be any kind of ambiguity in the arguments.

Eg: Statement : Should there be compulsory education up to Matric ?

Arguments : I. No , some persons don't have time to study.
II. Yes ,it will raise the standard of literacy.
Argument 1 is week But II is forceful.