Reverse Syllogism

Logical reasoning is an integral part of life and so with jobs as well. One of the very important parts of logical reasoning, therefore, is the syllogism, or the method of deducing inferences from the given data. Syllogism is of various types, as will be discussed later, and one of them is a reverse syllogism. Reverse syllogism means that conclusion will be given and one has to find the statements which could belong to the conclusion. The article describes syllogism in detail along with an exercise on the same. 

Syllogism (Greek) means inference or deduction. It is a form of logical or analytical reasoning consisting of some statements and conclusions based on them. The candidate has the job to relate what the statement says with what best conclusion that can be drawn from it. The exercise, therefore, tests one’s ability to make inferences given any situation and think logically and reasonably. 

Example- 

Statement- 

No panda is a dog. 

Some pandas are crows. 

All pandas are animals. 

Conclusion- 

1. Some dogs are crows.
2. Some crows are pandas. 
3. Some animals are not pandas. 

Solution- 

With the help of making a Venn diagram based on the given statements, the questions can be solved in minutes. So Statement 1 says no panda is a dog, statement 2 says some pandas are crows, and statement 3 says some animals are not pandas. 

Moving to conclusion number 1, some dogs are crow. This is not depicted in the Venn diagram, so that conclusion is not correct. Conclusion numbers 2 and 3, which say some crows are pandas and some animals are not pandas, respectively, are clearly visible in the Venn diagram. Therefore, conclusions 2 and 3 hold true. 

Venn Diagram

Venn diagrams are interesting ways of representing any information, using concentric circles to illustrate logical relationships between the data. Set diagrams or Venn diagrams/logical diagrams are commonly used in mathematics, statistics, logic, teaching, computer science, and business. Venn diagrams give a clear representation of the data and thus help in solving any glitches or missing information, if any, in the data.

 Source credits- lucidchart.com

Types of Syllogism

• Basic  syllogisme
• Here, the conclusion must be 100 percent true; any deviations from this will be considered false. 
• Either-or case syllogism

When the given conclusions are not 100 percent true, but the two given conclusions are 50 per cent true. 

• Coded syllogism

Here, the statement and conclusion are given in the coded form and the candidate has to decode the statement in order to answer the question and give the concluding answer. 

• Sequential syllogism

In this type, two statements are given with certain options following them. The candidate needs to choose the third statement going in synchronisation with the two statements. 

Reverse Syllogism

Reverse syllogism means that conclusions will be given and the candidate has to choose the correct statement which relates to the said conclusions. One of the good methods to answer reverse syllogism is the elimination method, wherein you eliminate one by one which doesn’t fit in. 

Example-

Conclusions:

(i) Some books are pens.

(ii) Some pencils are books.

Statements:

1. A) All books are paper. Some papers are pencils. No pencil is a pen.
2. B) All books are paper. No paper is pencil. All pencil is pen
3. C) Some books are paper. All papers are pencil. No pencil is a pen.
4. D) Some books are paper. All papers are pencil. All pencils are pens.

Solution– Option D 

Exercises

Q.1. Conclusion

(i) Some bats are not dogs.

(ii) Some bats are cats.

Statement

1. A) All dogs are cats. Some cats are bats. Some bats are rats.
2. B) Some dogs are cats. Some cats are bats. All bats are rats.
3. C) No dog is a cat. All cats are bats. Some bats are rats.
4. D) All dogs are cats. Some cats are bats. Some bats are rats

Q.2. Statement:

 Some actors are singers.

 All the singers are dancers.

Conclusion:

Some actors are dancers.

No singer is an actor.

1. Only (1) conclusion follows
2. Only (2) conclusion follows
3. Either (1) or (2) follows
4. Neither (1) nor (2) follows
5. Both (1) and (2) follow

Q.3. 

Answers

Q1. 

Ans- Option C

Q.2 

Ans- Option A

Q.3. 

Ans- Option D

Q.4. 

Ans- Option C 

Q.5. 

Ans- 1 and 2 

Conclusion

Syllogism is an interactive exercise to test your analytical thinking skills based on deducing inference from the given information. Based on what kind of statements and conclusions are, a syllogism can be of many types and every type is done based on a different strategy. Venn diagrams, however, remain a common way to solve such problems.