## Jun 18, 2015

### RULES FOR SOLVING SYLLOGISM PROBLEMS

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Rules for Solving Syllogism Problems.
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·
Conversion Rules:

1.) All à Some
For Eg. If All Cats are Rats, then
Some Rats are also Cats.
2.) Some àSome
For Eg. If Some Cats are Rats, then
Some Rats are also Cats.
3.) No à No/Some Not
For Eg. If No Cat is Rat, then
No Rat is Cat or Some Rats are not Cats.
4.) Some Not à Can’t be Converted.

·        Combination rules:

1) No Conclusion Combinations.

 S.No Statement 1 (A to B) Statement 2 ( B to C) Answer 1 All Some Some Not No Conclusion 2 No No Some Not No Conclusion 3 Some Some Some Not No Conclusion 4 Some Not Any No Conclusion

2) Conclusion Combinations.

 S.No Statement 1 (A to B) Statement 2 (B to C) Answer 1 All All No All (A to C) No (A to C) 2 No All Some Some Not (C to A) Some Not (C to A) 3 Some All No Some ( A to C) Some Not ( A to C)

Important Points:

To apply Combination Rules,
·        The both statement should be in proper format as given below à

Statement 1- A to B
Statement 2- B to C

i.e Middle term ‘B’ Should be same in the both given statements
·         And also the statements should contain only three including terms i.e A, B & C. If there are Four including terms present in the two given statements, For Eg,
If we have Given:
1)     All Cats(A) are Rats(B).
2)     All Monkeys (C) are Dogs(D).
then there is no need to check for the solution, we can direcly write the answer as ‘No Conclusion’.

Ø  If the statements are not in the proper format, then you have to first convert the given statement by using conversion rules before applying any combination rule.

Now take the example, If we have Given two statements as follow:
1)     All Cats(A) are Rats(B).
2)     Some Cats(A) are Dogs(C).

Above two statements are in the format:
1)     A to B
2)     A to C

So first convert the statement by using conversion rule to make them in proper format.

Now, the question is, which statement we should convert to make them in proper format?

Ø Priority order for Conversion of Statement:

1) Some
à 2) No à 3) All

So, now according to the priority order we should first convert the second statement i.e Some cats are Dogs à Some Dogs are Cats

Now the statement will be in the format à A to B & C to A.

1)     All Cats(A) are Rats(B).
2)     Some Dogs (C) are Cats(A).

They are still not in the given format. To make them in given format we have to interchange the positions of the statement i.e
1)     Some Dogs are Cats.
2)     All Cats are Rats.

Now, the middle term i.e Cats are same in both the statement & also there are three including terms. So, Now we can apply the combination Rule: Some + All = Some (A to C) & the answer will be Some Dogs are Rats.

·        Pairing rules:

 S.No Statement 1 (A to B) Statement 2 (A to B) 1 All Some Not 2 Some Some Not 2 Some No

For Making Pairs Remember Following Points:

1)     All Conclusion must be wrong.
2)     Variables of both the statements should be same.
3)     One statement should be positive & other should be negative.

·        Possibility Cases:

1)     If All A are B,
then Some B are not A is a Possibility.

2)     If Some B are Not A,
then All A are B is a Possibility.

3)     If Some A are B, then
All A are B is a possibility, or
All B are A is a Possibility.

4)     No Conclusion à Any possibility is true.

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