What is Syllogism?

Syllogism is a Greek word that means ‘inference’ or ‘deduction’.  In this form of reasoning, we draw a conclusion based on the two given or assumed propositions. 

For Example: 

Proposition 1: All A’s are B’s.

Proposition 2: All B’s are C’s.

From the above statements, we can conclude that All A’s are C’s

(The assumed propositions are also known as premises because the validity of a conclusion depends on them.)

 So, the problems of syllogism consists of two parts: 

1. Propositions (these are given to you)

2. Conclusion(s), that you need to draw based on the relationship existing between the different elements of the propositions.

It is easy to solve these problems using Venn Diagrams. Let’s see the Venn Diagram of the example mentioned above:

Syllogism: Venn Diagram Representation of the Example Problem
Venn Diagram Representation of the Example Problem

Logic behind drawing Venn Diagram: Based on the first proposition, which states All A’s are B’s, the circle representing A (the innermost one) lies within the circle representing B (the middle one). Similarly, based on the second proposition, the circle representing B lies within the circle representing C (the outermost one). 

From the Venn Diagram, we can clearly see that All A’s are C’s.

In this course, we will learn to solve syllogism problems using Venn Diagram approach only.

Your Turn:

Let’s practice what we have learnt. Assuming the statements given below to be true, draw a Venn Diagram to represent them and then using that write your conclusions.

Proposition 1: All horses are animals.

Proposition 2: All animals are beautiful. 

The problem is similar to the example we discussed in the text. The Venn Diagram will look like this: 

Syllogism: Practice Problem

From the Venn Diagram, we can infer that All horses are beautiful.

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