Syllogisms Concepts- Part I

4 Types of Statements:

a)Universal Statements (All Type Statements)

1)Universal Affirmative/Positive:

i.e. All A’s are B’s

Note: Converse All B’s Are A’s is a Possibility

2)Universal Negative : All A’s are not B:

 

Converse All B’s are not A

b)Particular Statements

 

3)Particular Affirmative/Positive:

 

Some A’s are B’s

 

Converse : Some B’s are A’s

4)Particular Negative:

Some A’s Are Not B

Converse : Some B’s are not A is a possibility

 

Learn the following tables with logic:

Other names of all, some, All not & possibilities

Important  Note:-

1.“Only A are B” means “All B’s are A’s” i.e. subject and predicate – change

2.“All A’s are definitely” means “All A’s are B’s”

3.“None but A is B” means Only A is B which in turn means “All B’s are A’s”

4. A is B means all A is B.

 

In each question there are five options available, learn these by heart but not necessarily in the same order.

1) only answer 1 is true

2)only answer 2 is true

3) either 1 or 2 is true

4) neither 1 nor 2 is true

5) both 1 and 2 are true.

This sequence will be used in the below questions…so do not get confused if numbers 1,2,3,4,5 are used in place of answer.

EITHER OR CONCLUSIONS:

(Qest.)

Some A’s are B’s

Some B’s are C’s

Conclusions :

Case (1)

(a) No A is C (F)

(b) Some A’s are C’s (F)  – (3)

Note : Here both statements are false  as from the diagram nothing definite can be known about relation b/w A and C had the word possibility added to the statements then they would have been true.

Case (2)

(a) No A is C is a possibility (T)

(b) Some As are C’s (F) – (1)

Case (3)

(a) No A is C (F) (2)

(b) Some A’s are C’s is a possibility (T)- (2)

Case (4)

(a) No A is C  is a possibility (T)

(b) Some A’s are C’s “     “  (T) – (5)

Conditions of Either Or :

(1) Subject Predicate should be same in both statements

(2) Complimentary pairs i.e. one should be positive and one should be negative

(3) Maximum possibility i.e. maximum diagrams possibility should be covered

(4) Individually both false

(5) relation between subject and predicate should not be clear.

(6) Either or condition not applicable between All and no type sentences.

i.e. All A’s are C’s (F)

No A’s are C’s (F) – then it is (4) and not (3)

But If it is:

All A’s are C’s

Some A’s are not C’s  (F) –the ans is (3)

OR

But if it is:

No A’s are C’s

Some A’s are not C’s- then ans is (4)

This is applicable between all & some statements

 

Note: No C is A can also be written as no A is C.

Similarly some A is C =some C is A.

So subject is equal to predicate.

 

ANOTHER METHOD FOR SOLVING SYLLOGISMS :

(Note : if method 1 is clear then you do not need this but never the less go through as it helps in clearing the concepts )

RULE METHOD ( learn by heart these)

Rule 1:

All + are  = All

Ex. All A’s are B’s

All B’s are C’s

Rule 2:

Some + All = some

Ex. Some A’s Are B’s

All B’s Are C’s

∴ Some A’s are C’s

Rule 3:

All + Some = no definite conclusion

Ex. All A’s are B’s

Some B’s are C’s

∴ Relationship between A and C is a possibility

Rule 4:

Some + Some = No definite conclusion

Rule 5:

Some + No = Some not (forward i.e. A to C)

Ex. Some A’s are B’s

No B’s are C’s

∴ Some A’s are not C’s

Rule 6:

No + Some = Some not (back words i.e. C to A)

Ex. No A’s are B’s

Some B’s are C’s

∴ Some C’s are not A

Rule 7:

No + No = no definite conclusion

Ex. No A’s are B’s

No B’s are C’s

∴ Relation between is a possibilities

Rule 8:

Some not + Some not = no definite conclusion (NDC)

Ex. Some A’s are not B

Some B’s are not C


Rule 9:

All + Some not = N D C

Rule 10:

Some + Some not = N D C

Rule 11:

Not + Some not = N D C

Ex:

Some Blue are Pink

All Pink are Orange

No Orange is White

Only Grey are White

 

1.Conclusion:

(a) No White is Orange

(b) Some Orange is Blue

 

2.Conclusion:

(a) Few White are Grey

(b) No Orange is Blue

 

3.Conclusion:

(a) Pink is White

(b) 100% White can be Orange

 

4.Conclusion:

(a) Some Pink are not White

(b) Grey can be White

 

5.Conclusion:

(a) Some Pink may be White

(b) Some White may be Blue

 

6.Conclusion:

(a) Some Blue are White

(B) No Blue is White

 

Ans.

(1)

(a) T

(b) T–(5)

 

(2)

(a) T

(b) F-(1)

 

(3)

(a) F

(b) F–(4)

 

(4)

(a) T

(b) T–(5)

 

(5)

(a) F

(b) T–(2)

 

(6)

(a) F

(b) F–(3)

 

(Q.)All Blue are Pink

No Pink is Orange

Only Blue are White

Some Pens are Boxes

No Boxes are Scales

 

Note :Whenever there are diagrams without relation then all statements whether positive or negative have to be with possibility.

 

(1) Some Pink are White

(2) Each Orange cannot be White

(3) Some Blue are Pens

(4) Some Boxes are pens as well as Scales

(5) No Orange is Scales

(6) Only Boxes can be Pens

(7) No White is Orange

(8) 0% Orange may be Blue

(9) Some Scales may be Blue & White

(10) All Pink Blue & White & Boxes being Scales is a possibility

(11) All Scales Pens & Orange being White is a possibility

(12) Almost Orange & Pink can be a combination part of pens & Boxes

 

Ans. (1) T, (2) F, (3) F, (4) F, (5) F, (6) T, (7) T, (8) F, (9) T, (10) F, (11) F, (12) T

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