How to solve problem on Syllogism in CAT Exam

Thursday, October 5th, 2017


Syllogism in CAT Exam

Syllogism is an influential concept of CAT. It has its role in logical reasoning and verbal ability section as well. There are approximately 3-4 questions based on it. And these many questions can play vital role in upgrading your percentile. Thus, it’s important that you understand this topic well so that you can score good in the exam. Let’s first understand what does syllogism mean and then I will tell you some useful techniques that will make solving questions on this topic a facile job for you.

Syllogism is a Greek synonym of the word conclusion or inference. A more proper definition of syllogism is an argument the conclusion of which is supported by two propositions, of which one contains the term that is predicate of the conclusion, and other contains the term that is subject of the conclusion; common to the both premises is the term that is excluded from the conclusion. Now, this definition of syllogism seems to be a bit confusing but, as this article proceeds you will one by one understand the deeper meaning of this definition.  Before illustrating the example of syllogism, first understand what is meant by proposition? A proposition is a sentence that makes a statement and gives a relation between two terms. Each proposition has three parts that forms the sentence structure i.e. subject, predicate and relation between both. Consider these two propositions:

Syllogism

Conclusion: All Rajasthani’s are Kind.

Let’s interpret the conclusion in terms of definition of Syllogism. Now in the sentence, All Rajasthani’s are Kind you can notice that the predicate of the proposition 2 became the predicate of conclusion (the word Kind) and the subject of the proposition 1 became the subject of conclusion (Rajasthani’s) and the common relation between the two (Indians) is missing from it. Thus, this conclusion exactly follows the definition of Syllogism. Now, you might have noticed use of word All in both the propositions. This type of proposition is called categorial propositions. The categorial proposition is further divided into two types.

Syllogism

Now the questions in the exam will consist of two or more propositions that will be followed up by two or more conclusions and you have to answer which conclusion follows the given propositions such as

Propositions: All tables are chalks.

All chalks are chairs.

Conclusions: All chairs are tables.

All tables are chairs.

Give answer:

1.    If only conclusion 1 follows.

2.    If only conclusion 2 follows.

3.    If either 1 or 2 follows.

4.    If neither 1 nor 2 follows.

5.    Both 1 and 2 follows.

Now the question arises how can we know that which of the above options is correct. There are two ways to determine that which conclusion will follow.

The Venn Diagram Method.

The Analytical Method.

Let’s first fathom the Venn Diagram method. We all have come across the Venn diagram as part of set theory in our high school math’s. But those of you who are still unaware of it, Venn diagram is a pictorial representation of mathematical or logic sets using circles or closed curves. Instead of directly hoping on devising the method first learn the representation of propositions using Venn diagram. As discussed earlier, there are two types of propositions Universal and Particular which are further distinguished into the positive and negative kinds of proposition respectively. These 4 kinds can be represented through Venn Diagram. Grab a look at the table below that illustrates the distinct types of propositions and its pictorial representation using Venn diagram.

Syllogism

The above propositions on the basis of above table can be summarized to following implications given below.

Syllogism

Using the above two tables we can easily form the conclusion from any number of propositions following two simple steps. Consider the example given above of tables, chairs and chalks. There are two propositions in the example:

Propositions: All tables are chalks.

All chalks are chairs.

Step 1: Draw Venn diagram of the both above propositions separately.

Now in this example, let T = tables, Chalks = CH, Chairs = CR. The first proposition says All tables are chalks. Therefore, it’s representation would be

Syllogism

Now analyze the figure and inspect which conclusions can be drawn from it. Here only second conclusion i.e. All tables are chairs is correct. Therefore, the right option of this question is only conclusion 2 follows. The Venn diagram method is very interesting and easy. The above example was a basic one but in exam questions will be more complex and complicated. You can solve them on the same lines as the above question using the two step Venn diagram method.

Let’s now move on the second one the analytical method. It is also two steps method. First consider another set of propositions and later come up with the conclusion.

Proposition: Some posters are good looking.

All posters are expensive.

Step 1: Aligning the given sentences.

Now by aligning it means that propositions should be written in such a way that the common term is the predicate of the first proposition and the subject of the second. In the above propositions, the common term is posters and for aligning we want that poster should be predicate of the first one. But here, it’s subject of proposition one. We will use conversion technique for that.

The rules for conversion are as follows: –

The subject becomes the predicate and the predicate becomes the subject.

The type of given proposition is changed according to the given table below.

A proposition of type When converted become proposition of type
I. III.
II. II.
III. III.
IV. These types cannot be converted.

Firstly, we will check that whether the propositions are aligned or not! Now in above example, the predicate of proposition 1 is not the subject of second one. Hence propositions are not aligned. So, for alignment we will convert the proposition 1 as using the above rules we get,

Proposition: Some good looking are posters.

All posters are expensive.

Step 2: Use the following table to draw conclusions.

If the first proposition is of type And the second proposition is of type Then the conclusion will be
I. I. I.
I. II. II.
I. III. No definite conclusion
I. IV. No definite conclusion
II. I. IV.*
II. II. No definite conclusion
II. III. IV.*
II. IV. No definite conclusion
III. I. III.
III. II. IV.
III. III. No definite conclusion
III. IV. No definite conclusion
IV. I. Or II. Or III. No definite conclusion

Note: IV. * means the conclusion is of type IV. But the format is directly opposite the standard IV. Type. In this case the subject of the conclusion is the predicate of second sentence and the predicate of conclusion is the subject of first proposition.

Again, let’s move to our example here in this case using the aligned propositions and using the above table we get III. + I. = I.

Therefore, the conclusion will be ‘Some good looking are expensive’.

In the above prescribed way, we can solve numerous analytical problem. Both the above method is equally efficient you can choose either of the one as per your convenience and understanding. Or, you can use both, one to solve the problem and other one to cross check the answer. But don’t waste too much time on this. Follow this practice only if you have ample of time left in exam or you are really confused.

Initially, you might face problems solving the problems of syllogism but with time and practice you will nail it!

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How to solve problem on Syllogism in CAT Exam

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