Syllogism Cheat Sheet

Dealing with syllogism had always been a big problem to me. Even if I do learn it how to deal with it, I often forget how to use them when required, I guess it needs constant revision and great logical and deductive reasoning capabilities to deal with.

Logical deductions

To make things easier, I keep this small cheat sheet which contain basic formulas to deal with syllogism in verbal reasoning. I will try to explain here, how to use this cheat sheet to solve the problems which often appears in competitive exams like CAT, XAT, IIFT, and nowadays even CSAT and other job oriented exams are also looking for reasoning capabilities in candidate.

First Premise Second Premise Conclusion
All All All
All No No
All Some No Conclusion
Some All Some
Some No Some Not
Some Some No Conclusion
No All “Some Not” – Reversed
No Some “Some Not” – Reversed
No No No Conclusion
“Some Not” or “Some Not” – Reversed Anything No Conclusion

You can use above table for your reference while solving problem on syllogism. Here is an example for same-

[Q] Premise Statements-
[a]. All cities are town.
[b]. Some cities are villages.
Conclusion Options-
[i]. All villages are town.
[ii]. No village is a town.
[iii]. Some villages are town.

Answer Options –

  1. Only conclusion [i] follows.
  2. Only conclusion [ii] follows.
  3. Only conclusion [iii] follows.
  4. None of these.

This is clearly a combination of All + Some in premise statements. Hence no conclusion can be drawn. So, option 4 is correct. None of these.

I had took this question from Combined Graduate Level Exam conducted by SSC in 2013, questions like this could be a matter of 2 or 3 seconds if you can remember this table. Here is another quick example of how to use this cheat sheet.

[Q] Premise Statements
(a). All papers are books.
(b). All books are pages
(c). All pages are material.
Conclusions Options:
I. Some material are pages.
II. All books are material.
III. All papers are pages.
IV. Some books are papers.

Answer Options –

  1. All the four follow.
  2. Only II, III follow.
  3. Only I, III and IV follow.
  4. Either I or III and II follow.
  5. None follows

This one is a bit tricky question. While it seems All + All = All, should give us II & III as correct statements, but we should also look what other statements are telling us. Conclusion statement I & IV are mere implications of premise statement (a) and (c). Hence the correct answer option is [1.] All the four follows.

And last but not the least, a very simple problem, which would generally come in medium difficulty level exam-

[Q]. Premise Statements-
Statement 1. Some dogs are bats.
Statement 2. All bats are cats.

You probably don’t need options for problem like this one, as you can refer the table above, which says Some + All = Some. So, cancelling out bats, we get Some dogs are cats as our answer statement…

There are plenty of various types of questions which one can practice based on Syllogism and deductive reasoning these generally include conditional statements, possibility cases, premise – conclusion etc. Sometimes conventional way of using Venn Diagram might help in solving Syllogism but not always a good practice in competitive exams. It would always be better if you could remember the various possibility cases, and arrive to conclusion in seconds instead of working out a problem in minutes. An advanced level cheat sheet for syllogism is available here.