Syllogism cheat sheet: Bank PO, SSC, UPSC-CSAT prep note

Dear readers,

Syllogism (deductive reasoning) is an important component of many banking entrance tests. However, many students find this topic quite confusing. Accordingly, on popular demand, I have prepared this cheat sheet for you. In this sheet, I have taken different pairs of statements (that commonly appear in such questions) and have listed out the important definite conclusions and possible conclusions that are valid for those statements. Just remember these and your work will be much easier when you come across syllogism questions in your exams.

Type 1:  

ALL + ALL 

Statements : 1.  ALL A are B.                                                 

                       2.  ALL B are C.

Certain Conclusion :    1. ALL A  are C.

Possible conclusions : 1. ALL B are A.

                                       2. ALL C are B.

                                       3. ALL C are A.

                                       4. SOME C are not B.

                                       5. SOME B are not A.

                                       6. SOME C are not A.

Type 2:

ALL + NO 

Statements :  1. ALL A are B.

                       2. NO B are C.

Certain Conclusion :  1.  NO A are C.

                                     2. NO C are A.

                                     3. NO C are B.

Possible conclusions :  1. ALL B are A.

                                        2. SOME B are not A.

Type 3:

ALL + SOME 

Statements :  1. ALL A are B.

                       2. SOME B are C.

Certain Conclusion :  SOME C are B.

Possible Conclusion :  1. ALL B are A.

                                      2. ALL B are C

                                      3. ALL A are C

                                      4. ALL C are B

                                      5. ALL C are A

                                      6. SOME A are C. 

                                      7. SOME C are A.

Type 4: 

NO + ALL 

Statements :  1. NO A is B.

                      2. ALL B is C.

Certain conclusion :  1. NO B is A. 

                                    2. SOME C are not A.

Possible conclusion :  1. SOME C is B.                     

                                     2. SOME A is C.

                                     3. SOME C is A.

                                     4. ALL C is B.

                                     5. ALL A are C

Type 5:

NO + SOME 

Statements :  1. NO A is B.

                       2. SOME B is C.

Certain Conclusion : 1. SOME C is B.

                                    2. NO B is A.

                                 3. SOME C is not A.

Possible Conclusion :  

                                   1. ALL B are C.

                                   2. ALL C are B.

                                   3. NO A is C.

                                   4. NO C is A.

                                   5. SOME C is A.

                                   6. SOME A is C.

                                   7. ALL A is C.

Type 6:

NO + NO 

Statements : 1. NO A is B.

                     2. NO B is C.

Certain Conclusion : 1. NO B is A.

                                  2. NO C is B.

Possible Conclusion : 1. NO A is C.

                                      2. NO C is A.

                                      3. SOME A is C.

                                      4. SOME C is A.

                                      5. ALL A are C.

                                      6. ALL C are A.

Type 7:

SOME + ALL 

Statements : 1. SOME A are B.

                       2. ALL B is C.

Certain Conclusion : 1. SOME B is A.

                                    2. SOME C are B.

                                    3. SOME A are C.

                                    4. SOME C are A.

Possible Conclusion : 1. ALL C is A.

                                     2.  ALL B are A.

                                     3.  ALL A are C.

                                     4. ALL C is B.

                                     5. SOME C is not B.

                                     6. SOME C is not A.

Type 8:

SOME + SOME 

Statements :  1. SOME A are B.

                       2. SOME B are C.

Certain Conclusion :  1. SOME B are A.

                                     2. SOME C are B.

Possible Conclusion : 1. SOME C are A.

                                      2. SOME A are C.

                                      3. ALL C are B.

                                      4. ALL B are A.

                                      5. ALL C are A.

                                      6. ALL A are C.

                                      7. SOME C are not B.

                                      8. SOME B are not A.

                                      9. SOME A are not C.

                                     10. SOME C are not A.

                                     11. NO A are C.

                                     12. NO C are A.

Type 9:

SOME + NO 

Statements : 1. SOME A are B.

                       2. NO B are C.

Certain Conclusion :  1. SOME B are A.

                                     2. NO C are B.

                                     3. SOME A are not C.

Possible Conclusion : 1. SOME C are A. 

                                      2. SOME A are C.

                                      3. ALL B are A.

                                      4. ALL C are A.

                                      5. ALL A are B.

                                      6. SOME C are not A.

                                      7. NO C are A.

                                      8. NO A are C.

Read Next