13 Syllogism Study Materials

SYLLOGISM

Following are the main rules for solving Syllogism Problems

Rule-1.All+All=All

Rule-2.All+No=No

Rule-3.All+Some=No Conclusion

Rule-4.Some+All=Some

Rule-5.Some+No= Some Not

Rule-6.Some+Some= No Conclusion

Rule-7.No +All = Some Not(Reversed)

Rule-8.No+Some=Some Not (Reversed)

Rule-9.No+No=No Conclusion

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

If u want to convert any conclusion in Possibility

Rule-11.If - All A are B then we can say - Some B are Not A is a Possibility

Rule-12.If - Some B are Not A then we can say - All A are B is a Possibility

Rule-13.If - Some A are B then we can say - All A are B is a Possibility All B are A is a Possibility

Rule-14.All �Some Not Reversed

Rule-15.Some => All

Rule-16.NO Conclusion = Any Possibility is true

Implications (In case of Conclusion from Single Statement)

All =>  Some  - that means if All A are B then Some B are A is true

Some �Some  -that means if Some A are B then Some B are A is true

No � No  -   that means if No A is B then NO B is A  is true

There are Two Major Ways to solve syllogism questions �

Cross Cancellation and Vertical Cancellation

Example 1. Cross Cancellation

Statements

1.All forces are Energies

2.All Energies are Powers

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

All Energies are Powers

No Power is Heat

This will be called Cross Cancellation , 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

All forces are Energies

All Energies are Powers

No Power Is Heat

[All+All=All ; All+No=No]

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

Solution - Lets take 1st Conclusion �All Mails Being Update is a Possibility� that means we have to make relation between Mails and Updates

Some Mails are Chats

All Updates are Chats

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 Don�t .