Syllogism : Verbal reasoning

Updated: Aug 26

syllogism reasoning concept and reasoning syllogism quiz


Following are the main rules for solving Syllogism Problems

  1. All+All=All

  2. All+No=No

  3. All+Some=No onclusion

  4. Some+All=Some

  5. Some+No= Some Not

  6. Some+Some= No Conclusion

  7. No +All = Some Not(Reversed)

  8. No+Some=Some Not (Reversed)

  9. No+No=No Conclusion

  10. Some Not /Some Not Reversed +Anything = No Conclusion

If u want to convert any conclusion in Possibility

11. If All A are B, then we can say – Some B are not A is a Possibility.

12. If Some B are not A, then we can say – All A are B is a possibility.

13. If Some A are B, then we can say – All A are B is a Possibility and All B are A is a Possibility.

14. All Some <———> Not Reversed

15. Some <———-> All

16. NO Conclusion = Any Possibility is true

Implications (In case of Conclusion from Single Statement)

How to solve questions using above rules? There are two rules to solve syllogism questions – Cross Cancellation and Vertical Cancellation Example 1. Cross Cancellation Statements 1.All forces are Energies 2.All Energies arePowers 3.No Power is Heat Conclusions 1.No Energy is Heat 2.Some Forces being heat is Possibility Solution – Lets take 1st conclusion, we have to make relation between Energy and Heat so we will take statement 2 and 3

This will be called Cross Cancelation, We have cancelled power from Power so we have left with (ALL+NO) Energies is/are Heat, and that is No Energy is Heat. So Conclusion First is TRUE.

In second statement we have Force and Heat so we will need to make relation between force and heat. For this we need to take all 3 statements

Now we have left with ((All+All)+NO) Forces is/are Heat and that is NO Force is Heat . We don’t have any rule to convert this statement is Possibility so second conclusion is FALSE

Example 2 – Vertical Cancellation Statements: 1. Some Mails are Chats 2. All Updates are Chats Conclusion: 1. All Mails being update is a possibility 2. No update is Mail Let’s take 1st Conclusion “All Mails Being Update is a Possibility” that means we have to make relation between Mails and Updates

This is called vertical cancellation. In this case direction of adding first phrase will be reversed i.e In Above example the conclusion will be (All+Some) Updates is/are Mails = No Conclusion . If we get No Conclusion in case of Possibility then according to Rule No 16 possibility case will be definitely true . So Conclusion 1 follows and Conclusion 2nd Doesn’t follows. SOME NOT REVERSED: Let’s Take an Example No A is B All B is C So the conclusion will be (No + All) A is C = (Some Not Reversed) A is C = Some C are Not A.