Syllogism is a kind of logical argument that applies deductive reasoning to arrive at conclusion based on two or more propositions that are asserted or assumed to be true.

Example :

- All roses are flowers
- All flowers are beautiful
- All roses are beautiful

Clearly the proposition 1 and 2 are the premises and the proposition 3, which follows from the first two propositions is called the conclusion.

**Term : **In logic, a **term** is a word or a combination of words, which by itself can be used as a subject or predicate of a proposition.

Syllogism is concerned with three types:

**Major Term:**It is the predicate of the conclusion and is denoted by P (“Predicate”)**Minor Term :**It is the subject of the conclusion and is denoted by S (“Subject”)**Middle Term**: It is the term common to both the premises and is denoted by M (“Middle”)

In the above example, beautiful is predicate of the conclusion and roses are the subject of the conclusion; flowers are the common term for both premises hence it is the Middle.

**Major and Minor Premises:**

Of the two premises, the **Major Premise **is that in which the middle term is the subject and the **Minor Premise **is that in which the middle term is the predicate.

**Rules for deriving the conclusion from two given premises**

**1. The conclusion does not contain the middle term.**

**2. No term can be distributed in the conclusion unless it is distributed in the premise.**

**3. The middle term (M) should be distributed at least once in the premises. Other wise the conclusion cannot follow.**

For the middle term to be distributed in a premise,

- M must be the subject if premise is an A proposition
- M must be subject or predicate if premise is an E proposition
- M must be predicate if premise is an O proposition.

Note that in I proposition, which distributes neither the subject nor the predicate, the middle term cannot be distributed.

*Ex. Statements : 1. All fans are watches 2. Some watches are pink*

*Conclusion : 1. All watches are fans 2. Some fans are pink*

*In the premise, the middle term is not distributed in the first premise which is an A proposition as if does not form its subject. Also, it is not distributed in the second premise which is an I proposition. Since the middle term is not distributed even once in the premises, so no conclusion follows.*

**4. No conclusion follows :**

**if both the premises are particular****if both the premises are negative****if the major premise is particular and minor premise is negative**

**5. If the middle term is distributed twice, the conclusion cannot be universal.**

**6. If one premise is negative, the conclusion must be negative.**

**7. If one premise is particular, the conclusion must be particular.**

**8. If both the premises are affirmative, the conclusion must be affirmative.**

**9. If both the premises are universal, the conclusion must be affirmative.**