Syllogism in CAT exam come in the DILR (Data Interpretation and Logical Reasoning). However, sometimes, it also appears in the VARC (Verbal Ability and Reading Comprehension) section of the test. These concepts appear as 3-4 questions. Thus, they play an important role in defining your overall percentile. Consequently, it’s essential for a student to understand this topic well in order to score well.
So, many students do not know what syllogism is and how to go about the questions related to it. This article serves as guide for all of your doubts related to CAT-level syllogism.
What are Syllogisms?
Syllogism is actually a word of Greek origin which means conclusion, conjecture, or inference. In the logical reasoning domain, Syllogism means a proposed argument. This argument is supported by two propositions. One of the propositions is the predicate of the conclusion, while the other is the subject of the conclusion. This conclusion is apparently drawn from the proposed argument, i.e, Syllogism. This, of course, sounds too confusing, doesn’t it?
Let’s understand what is what first. So, what exactly is a proposition?
A proposition is a statement that gives relation between two terms. Furthermore, This proposition has three components in its statement: Subject, predicate and the relation.
Let’s take an example to understand this better.
- All papers are A4-sized
- All A4-sized papers are white
Here, in the sentences given above, “papers” and “A4-sized papers” are subjects of the statements. Meanwhile, the predicates of the statements are “A4-sized” and “white”.
By syllogism’s common definition, the above given example is apt. If you observe the above examples carefully, you’ll notice the following:
- There’s no direct relation between the subject of the first statement and the predicate of the second statement.
- However, the predicate of the first statement becomes the subject of the second statement.
- Both of the statements use the word “All”
The above pattern mentioned is typical of syllogisms. Although, the word “All” is used in both of the statements, this is not common practice. It mostly depends on the type of the propositions. So, the type in which ‘All’ is used is categorial proposition.
Types of Propositions
Categorial Propositions are further classified into two types: Universal proposition and Particular proposition.
1. Universal Proposition: These kinds of propositions either are completely inclusive or exclusive of a category or subject.
Example:
- No Indian uses chopsticks. (negative)
- All Koreans use chopsticks. (positive)
2. Particular Proposition: These kinds of proposition either partially include or exclude a category or subject.
- Some mangos are raw. (positive)
- Not all raw mangos are sour. (negative)
- Some mangos are not sweet. (negative)
Methods to Solve Syllogisms for CAT
There are two methods to solve syllogisms:
- The Venn Diagram Method
- The Analytical Method
The Venn Diagram Method
We have all learnt the concept of Venn Diagrams as part of set theory in our school days. However, if you still don’t remember them, Venn Diagrams are a pictorial representation which uses circles or closed loop to represent mathematical or logical sets.
So, let’s first look into how Venn Diagrams represent different types of propositions.
Types of Propositions | Universal/ Particular | Venn Diagram | Explanation |
Positive | 1^{st} type: All Y are Z. | The statement says that All Y are Z. Thus, it implies that Y is a subset of Z, a superset. | |
Positive | 2^{nd} type: Some Y are Z. | There are two scenarios here: either Set Y intersects with Set Z or Set Z is a subset of superset Y. | |
Negative | 3^{rd} type : No Y are Z. | The statement states that no Y are Z. Therefore, Set of Y and Set of Z do not intersect at all. They remain apart as two separate sets. | |
Negative | 4^{th} type:
Not all Y are Z; some Y are not Z. |
Two scenarios are possible for this condition: either Set of Y and Set of Z intersect, or Set of Z is a subset of the superset of Y |
Using the above method, we can come to the following conclusions:
Type of Proposition | The type of the proposition in the expectant conclusion | |||
1^{st} type | 2^{nd} type | 3^{rd} type | 4^{th} type | |
1^{st} type | — | False | True | False |
2^{nd} type | False | — | False | True |
3^{rd} type | Not sure | False | — | Not sure |
4^{th} type | False | Not sure | Not sure | — |
Example:
All pencils are erasers
All erasers are latex
Conclusion:
a. All latex are pencils
b. All pencils are latex
Options:
(a) Only conclusion a is true
(b) Only conclusion b is true
(c) Neither conclusion a nor b is true
(d) both conclusion a and conclusion b are true.
Approach:
1) Draw two separate Venn Diagrams of the statements.
2) Now, P = pencils and E = Erasers. So, as all pencils are erasers, it implies that P is a subset of Set E.
3) Then, L = latex. As all erasers are latex, E is a subset of the superset L.
In the end, we should get a figure as such:
On analysing the final Venn Diagram, we can say that only conclusion b follows. Therefore, the correct option is (b).
The Venn Diagram is practical and helps a student avoid conclusion. Using this two-step Venn Diagram, you can solve any syllogism question easily.
The Analytical Method
Q. Some Indians are brown
All Indians are kind.
Approach:
1) Convert Statements in a way that the common term in both the statements is the predicate of the proposition and the subject of the second statement.
In the above propositions, the common term is Indians. So, let’s align Indians as the predicate of the first statement. This conversion can be done by using the table below.
Type of Proposition | Type of the Proposition converted |
1^{st} type | 3^{rd} type |
2^{nd} type | 2^{nd} type |
3^{rd} type | 3^{rd} type |
4^{th} type | Not possible to convert |
So, as the first statement is of type 2, it will be converted into type 2 . The converted statement is “Some browns are Indians”.
After aligning the statements:
Some browns are Indians.
All Indians are Kind.
2) Now, you can use the table given below to draw conclusions after the conversion.
No conclusion combinations:
The type of the first proposition | The type of the second proposition | The conclusion |
1^{st} type | 3^{rd} type | No conclusion |
1^{st} type | 4^{th} type | No conclusion |
2^{nd} type | 2^{nd} type | No conclusion |
2^{nd} type | 4^{th} type | No conclusion |
3^{rd} type | 3^{rd} type | No conclusion |
3^{rd} type | 4^{th} type | No conclusion |
4^{th} type | 1^{st} type or 2^{nd} type or 3^{rd} type | No conclusion |
Definite Conclusion Combinations:
The type of the first proposition | The type of the second proposition | The conclusion |
1^{st} type | 1^{st} type | 1^{st} type |
1^{st} type | 2^{nd} type | 2^{nd} type |
2^{nd} type | 1^{st} type | 4^{th} type* |
3^{rd} type | 1^{st} type | 3^{rd} type |
2^{nd} type | 3^{rd} type | 4^{th} type* |
3^{rd} type | 2^{nd} type | 4^{th} type* |
Note*: The conclusion you get for the type-4 when either type-2 and type-1 combine or type-2 or type-3 combine is opposite to the standard format of type-4.