Syllogism is considered one of the confusing topics in Reasoning. The questions along with the options look simple enough to lure candidates to answer them. But if the concepts are not clear, these questions can attract negative marking. You need to be cautious enough to answer these questions. You can expect some questions on this topic in IBPS PO, NIACL Assistant and Indian Bank, a majority of which is easy, scoring and takes less time. Syllogism is all about concluding one or more statement(s) with the help of previous statements.

Let’s try to understand the different concepts of Syllogism with the help of the Venn Diagram. Please note that we have exhausted all the possibilities where only one statement is there (for eg. Some P are Q). But in multiple statements (for eg. 2. Some P are Q and some Q are R), there are many other options which we’ll not be able to cover because of space constraints.

1. Some P are Q

This is one of the most generalized statement. It says that some P are Q but doesn’t really tell us how much of P (may be the complete Q is P) is Q. You need to think about all the probabilities when you see this statement.

Conclusions:

  1. Some P are Q
  2. Some Q are P

2. Some P are Q and some Q are R

Conclusions:

  1. Some P are Q
  2. Some Q are P
  3. Some Q are R
  4. Some R are Q

Since there isn’t any connection mentioned between P and R so it’s not possible to conclude anything about them. But between Some “P are R” and “None of P is R”, we know that either of these conclusions has to be true. Either P and R will have a connection or it won’t have a connection.

3. All P are Q

Conclusions:

  1. All P are Q
  2. Some P are Q
  3. Some Q are P

4. All P are Q and all Q are R

Conclusions:

  1. All P are Q
  2. All Q are R
  3. All P are R
  4. Some P are Q
  5. Some Q are P
  6. Some Q are R
  7. Some R are Q
  8. Some P are R
  9. Some R are P

5. Some P are Q. All Q are R

Conclusions:

  1. Some P are Q
  2. Some Q are P
  3. All Q are R
  4. Some Q are R
  5. Some R are Q
  6. Some P are R
  7. Some R are P

6. All P are Q, Some Q are R

Conclusions:

  1. All P are Q
  2. Some P are Q
  3. Some Q are P
  4. Some Q are R
  5. Some R are Q

Since there isn’t any connection mentioned between P and R so it’s not possible to conclude anything about them. But between Some “P are R” and “None of P is R”, we know that either of these conclusions has to be true. Either P and R will have a connection or it won’t have a connection.

7. All Q are P, All R are P

Conclusions:

  • All Q are P
  • Some Q are P
  • Some P are Q
  • All R are P
  • Some R are P
  • Some P are R

Since there isn’t any connection mentioned between Q and R so it’s not possible to conclude anything about them. But between “Some Q are R” and “None of Q is R”, we know that either of these conclusions has to be true. Either Q and R will have a connection or it won’t have a connection.

8. No P is Q

Conclusions:

  • No P is Q
  • No Q is P
  • Some P is not Q
  • Some Q is not P

9. All P are Q, No Q is R

Conclusions:

  • All P are Q
  • Some P are Q
  • Some Q are P
  • No R is Q
  • No Q is R
  • Some R is not Q
  • Some Q is not R
  • No R is P
  • No P is R
  • Some R is not P
  • Some P is not R

10. All P are Q, No P is R

Conclusions:

  • All P are Q
  • Some P are Q
  • Some Q are P
  • No P is R
  • No R is P
  • Some P is not R
  • Some R is not P
  • Some Q is not R

11. Some P are Q, No Q is R

Conclusions:

  • Some P are Q
  • Some Q are P
  • No Q is R
  • No R is Q
  • Some R is not Q
  • Some Q is not R
  • Some P is not R

12. Some P are Q, No P is R

Conclusions:

  • Some P are Q
  • Some Q are P
  • No P is R
  • No R is P
  • Some P is not R
  • Some R is not P
  • Some Q is not R

Usage of ‘Possibility’ and ‘Can’

Sometimes, questions have the word possibility and can. Whenever you face this kind of question, see if there is any statement which is outrightly negating it. If no negation is there, the possibility is definitely there. You can also remember the below rules:

Statement: All P are Q

Conclusion:

  • All Q being P is a possibility
  • Some Q is not P is a possibility

Statement: Some P are Q

Conclusion:

  • All Q being P is a possibility
  • All P being Q is a possibility
  • Some P is not Q is a possibility
  • Some Q is not P is a possibility

Statement: Some P is not Q

Conclusion:

  • All Q being P is a possibility
  • No P is Q is a possibility
  • No Q is P is a possibility
  • Some Q is not P is a possibility
  • Some P are Q is a possibility
  • Some Q are P is a possibility

Final Word:

Syllogism is a simple concept if you remember the above rules and practice different kinds of questions. Sometimes the questions will try to confuse you by putting such names which are interrelated. For eg. Some pages are papers. No paper is book. You shouldn’t assume that there is some existing relationship between pages, papers, and books and start solving the question with a clean slate. If enough practice via mock tests is done, it’s all a matter of drawing diagrams quickly and answering questions correctly.


    A Range of Mock Tests

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