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# Reasoning - Syllogism

The meaning of syllogism as given by Greeks is **Deduction**. It’s a kind of logical argumentation.

### Definition of some important terms

There are some terms given below which have important role in solving problems on syllogism.

**Proposition**− proposition is a sentence which makes statements. Proposition consists of 3 parts these are a) subject, b)predicate and c) the relation between subject and predicate. Some propositions are given below.- All coasts are beaches.
- No students are honest.
- Some documents are secret.

**Subject and Predicate**− Subject is that part about which something is being said. On the other hand, predicate is the part which is related to subject. For example − from the above propositions coasts, students, documents are subjects while beaches, honest, and secret are predicates.

### Types of Categorical Proposition

**Universal Proposition**− Universal proposition is that which either includes subject fully or exclude it entirely. For example- No students are brainy. Universal proposition is further classified into following −**Universal positive proposition**− When the form is**all X are Y**then it is called positive proposition. It is generally denoted by letter**A**.**Universal negative proposition**− When the form is**no X are T**, then it is called as negative proposition. It is denoted by**E**.

**Particular proposition**− It is the proposition that shows subject partially or exclude it partly but not completely. For instance, some cats are cotton. It is also divided into following types −**Particular positive proposition**− Forms like**some X are U**are called particular positive proposition. They are coded as**I**.**Particular negative proposition**− Forms like**Some T are not P**for Instance,**some cats are not coils**is called particular negative proposition and coded as**O**.

**Mediate inference**− Here conclusion is taken from two statements. Example − “all lips are coils” and “all balls are bats”. So the conclusion will be “all lips are coils”.**Immediate inference**− Here conclusion will be taken from only one proposition. For instance, if the statement is “all teachers are god” then conclusion will be “some teachers are god”.

### Two important methods of immediate inference

These methods include conversion, contraposition etc.

**Implications**− Suppose given that “all cats are beaches”, then it shows that the conclusion “some cats are beaches” is true. So if a given proposition is of A-category, then it also shows that I-type conclusion must be true.**Conversion**− It consists of 2 steps.**Step 1**− The subject will be converted into predicate and vice versa.**Step 2**− The proposition which is given will be changed accordingly.

**For Example −**

**Statements** − All the cats are racks. All the bags are racks. Some purses are bags.

**Conclusions** −

1. Some cats are bags.

2. Some racks are cats.

3. Some racks are purses.

**A** - Only 1

**B** - Only 2 and 3

**C** - Only 1 and 2

**D** - Only 1 and 3

**Solution −**

Answer - Option B

Pictorial way of representing propositions are formulated by Euler. There are four ways in which the relation could be made according to four propositions.

Type − A stands for “All X are Y”, Type − E stands for “No X are Y”, Type − I stands for “Some A are B” and Type − O stands for “Some X are not Y”.

**For Example −**

**Statements −**

Some cameras are laptops.

Some laptops are phones.

Some phones are tablets.

**Conclusions −**

I - At least some tablets are cameras

II - There is a possibility that all tablets are laptops

III - None of the tablets are laptop

**Solution −**

Circle Diagram −

As per the above diagram,

Conclusion III follows. But ‘possibility’ word has been mentioned in the statement. So let’s check for the possibilities.

New diagram will be −

But in this case, conclusion III does not follow. Either conclusion II or conclusion III follows.