Inductive reasoning: syllogisms: easy method, tips and tricks to solve syllogisms

syllogism_example

WHAT IS SYLLOGISM?

A syllogism is a kind of logical argument in which one proposition (the conclusion) is inferred from two or more others (the premises).

example:

Premise 1: All women are mothers.

Premise 2: All mothers are caring.

Conclusion: All women are caring.

All of us, who have given or are preparing for any kind of entrance exam like CAT, SSC, MAT, XAT, SCAT and others, have come across syllogisms. Venn diagrams are used to solve syllogisms and are considered the standard way. But Alas! our exams’ time limit does not provide us with the time enough to draw the diagram, label and shade it and draw the conclusion out of it!

Then!! What to do?

Well there is not much to worry. Here are some basic tips, tricks and step by step method which will help you to solve a syllogism or at least make it somewhat easier.

  1. Shortcut rules (if Venn Diagrams are confusing you) between Statement 1 and Statement 2 in that order

 All + All = All

All + No = No

All + Some = No Conclusion

Some + All = Some

Some + Some = No Conclusion

Some + No = Some Not

No + No = No Conclusion

No + All = Some not reversed

No + Some = Some not reversed

2. You can cancel out common terms in two statements given, then on the remaining terms apply the syllogisms rules and solve. E.g. Some dogs are goats. All goats are cows.out “goats” which leaves us with Some dogs are…all are cows. Important words remaining are SOME and ALL in that order. SOME + ALL = SOME, hence conclusion is SOME dogs are cows.

3. Avoid using common knowledge as Syllogisms questions usually state unnatural statements.

4. Remember some implications

All <=> Some, e.g. All A are B also implies Some A are B (being a subset) and Some B are A

Some <=> Some, e.g. Some A are B also implies Some B are A

No<=> No, e.g. No A are B also implies No B are A

STEP 1: CLASSIFICATION OF STATEMENTS:

In syllogism, each statement usually has following format:

“xyz subject is/are (not) predicate.”

For example,

Xyz Subject Is/are (+/-not) Predicate
All Cats Are Dogs
Some Pigs Are not birds

Based on “xyz” and “not”, we classify the statements as following

Statement Type Codename
1. All cats are dogs Universal Positive UP
2. Some dogs are birds Particular Positive PP
3. No bird is a pig Universal Negative UN
4. Some pigs are not birds. Particular Negative PN

Please remember following words. Whenever they come, you classify the statement accordingly.

All, every, any, none, not a single, only etc. Universal (positive or negative)
Some, many, a few, quite a few, not many, very little, most of, almost, generally, often, frequently, etc. Particular (positive or negative)

STEP 2: STANDARD FORMAT: CONVERSION(important: priority order for conversion is PP>UN>UP.)

Basically, a syllogism(we consider 2 premise syllogism here) should have the following basic form:

1. A—>B

2. B—>C

If it is not, then it needs to be converted to the above format.

NOTE:

Question statements must have ONLY three terms. (A, B and C).

In the exam, if they give you two question statements with four terms then your time is saved! Just tick the answer “no conclusion can be drawn”.

For example

Question statements Answer
1. All cats are Dogs

2. Some birds are pigs

No conclusion can be drawn. Because it has four terms (cats, dogs, birds, pigs)

A–>B

C–>D

CONVERSION:

Ok, so how to convert the statements?

Universal Positive (UP)

Given Statement Valid conversions Type
Given Statement: All Cats are Dogs Some Cats are dogs Particular Positive (PP)
Some dogs are cats Particular Positive (PP)

It means UP can be converted into PP.

Please note: if the statement is “Only Dogs are cats”, then better convert it into “All cats are dogs”. (Only A is B –> All B are A)

Universal Negative (UN)

Given Statement Valid conversions Type
Given Statement: No Cats are Dogs Some dogs are not cats Particular Negative (PN)
No dogs are cats Universal Negative (UN)

It means UN can be converted into PN or UN.

Particular Positive (PP)

Given Statement Valid conversions Type
Some Cats are Dogs Some dogs are cats Particular Positive (PP)

It means PP can be converted into PP only.

Particular Negative(PN)

Example: Some Cats are not Dogs. In Particular negative statements (PN), no conversion can be made.

To sum up the conversion rules

Type Valid Conversion
Universal Positive (UP) Only PP
Universal Negative (UN) PN or UN
Particular Positive (PP) Only PP
Particular Negative (PN) Not possible.

 

STEP 3: NO CONCLUSION COMBOS

Here are the non-conclusion combos when two question statements are in following format.

First statement (A to B) Second statement (B to C) Answer
Universal Positive (UP) Particular Positive (PP) No conclusion
Particular Negative (PN) No conclusion
Universal Negative (UN) Universal Negative (UN) No conclusion
Particular Negative (PN) No conclusion
Particular Positive (PP) Particular Positive (PP) No conclusion
Particular Negative (PN) No conclusion
Particular Negative (PN) Any other (UP, UN, PP, PN) No conclusion

^does it look difficult?

Not really. Let’s condense this table into mug-up rules.

  1. UP’s politicians hate giving particular statements (both positive and negative). E.g. they do not reveal their clear position on FDI in retail until the 11th hour.
  2. United Nations hates negativity. (both Universal and particular)
  3. Pritish Nandy hates everybody.
  4. Two-negatives=no conclusion. (although implicit in 2+3)
  5. Two particulars=no conclusion. (although implicit in 1+3)

STEP 4: CONCLUSIVE COMBOS

First statement (A to B) Second statement (B to C) Conclusion
Universal Positive (UP) Universal Positive (UP) Universal Positive (UP) (A to C)
Universal Negative (UN) Universal Negative (UN) (A to C)
Universal Negative (UN) Universal positive (UP) Particular Negative (PN). (C to A)
Particular Positive (PP)
Particular Positive (PP) Universal Positive (UP) Particular Positive (PP) (A to C)
Universal Negative (UN) Particular Negative (PN) (A to C)

As you can see from above table,

The answer statement is usually in the format of A to C. with exception when first question statement is Universal Negative (UN).

Let’s condense this table into mug-up rules as well.

Conclusive-Combos In your head, visualize
  1. UP+UP=UP
If Uttar Pradesh meets Uttar Pradesh, then its size doesn’t increase.
  1. UP+UN=UN
If Uttar Pradesh meets United Nations then its size increases and it becomes United Nations.
  1. UN+ (UP/PP)=PN
United Nations Secretary Ban Ki Moon is in very positive mood. But he meets another positive person, and his attitude is totally reversed- he becomes particularly negative! (reversed =C to A)
  1. PP+ (UP/UN)=PP/PN
When Mr.PP observes the universe via NASA telescope, his mood becomes positive or negative depending on the mood of universe.

Following the above mentioned 4 STEPS and remembering some tips and tricks, you will be able to solve syllogisms in an easy and less time consuming way.

Hit like if you found the post useful… Hope it helps you!

Thanks

All the best!!!

Need a break from studies? Visit this creative blog: Kiddie Wing

This entry was posted in easy and shortcut method to solve syllogisms, reasoning, syllogism and tagged , . Bookmark the permalink.

172 Responses to Inductive reasoning: syllogisms: easy method, tips and tricks to solve syllogisms

  1. vidya says:

    very helpful!! Thank yu so much..:)

  2. jahnavi says:

    Hi pallavi ji
    Thanks for ur tips and tricks
    and really they are helping a lot in solving syllogisms in short time.
    can u plz explain me this ?
    statements : all bags are chalks
    all chalks are bottles
    conclusion : 1.some bottles are bags
    2. all bags are bottles
    3. all bottles are bags
    4. some chalks are not bags
    answer for this question in rs agarwal book is con 1,2,4 follows
    i know conclusion 1,2 follos but how come conclusion 4 follows?
    plz clarify this

  3. jahnavi says:

    thank u very much.
    i understood it now

  4. jahnavi says:

    stmts : all trolleys are pulleys
    some pulleys are chains
    all chains are bells
    con :
    1.some bells are trolleys
    2.no bell is trolley
    3.some pulleys are bells
    4.all chains are pulleys
    i know tat con 3 follows
    but in rs agarwal they gave either 1 or 2, and 3 follows
    can u plz explain this tat how come con 1,2 follows?

    • Tilak says:

      Hi Janhvi,
      U hav forget to chk either or pair…1 When both conclu. is worng and one positve and one negative and one must be particular then either or case applied. Hence Either 1 or 2 as well as 3rd follow.. chek original post at mrunal.org

    • pradeep says:

      janvi g simpil h .. ya to bells trolleys hongi ya nhi hongi… koi 3 chij to ho nhi sakti .. so either aya..

  5. jafar says:

    i hav a doubt ji
    1.all goats r cows
    some goats r lambs
    conc1: all goats r lambs
    conc2:some lambs r cows ANSWER ME ,A->B coversion must or not??and my book answer is CONC2 follows,but ur method shows NO CONC… plz reply???!

    • jafar says:

      answer me pls……all r getting wrong ans.
      SOME+SOME and ALL+SOME

      • Bs Rokhum says:

        Venn diagram will help u in this case..sometimes we have to follow the rules & tricks, at the same time we have to have alternative solution too.
        There are some statement which we can easily conclude even before applying methods-
        see- if all goats are lambs, i am sure about the possibility of some lambs are cow Because All goats are cow…everything which has a relation with goats will effect Cow.

      • KARTHI says:

        change the second sentence into “some lanbs are goats”
        now all goats are cows

        now if you notice some lamps are cows must follow

  6. Prakash Agrawal says:

    very nice tips and tricks….
    so much thanks……

  7. Prakash Agrawal says:

    All the pencils are inks.
    Some inks are pencils.

    wath is the solution of this question

  8. Aditya says:

    hi jahnavi:
    therecan be two different cases
    1st : some pulleys are chains include trolley
    2nd : some pulleys are chain does not include trolley

    so if 1st case is true then conclusion 1 follows and if 2nd case is true then conclusion 2 follows

    in either case conclusion 3 follows and 4 doe snot
    so either 1 or 2 and 3 follows

  9. Sg says:

    Please Give me a example of syllogism with this…
    No + All = Some not reversed
    No + Some = Some not reversed
    Thank you

    • DAMU says:

      No + All = Some not reversed:::

      Statement : No table is a furniture, All furniture are toys
      Conclusion : some toys are not tables

      No + Some = Some not reversed:::

      Statement : No chair is a table, Some tables are furniture
      Conclusion : Some furniture are not chairs

  10. Sg says:

    Please help me to solve this
    1.All apartments are huts.
    2. No hut is a building.
    3 . All buildings are cottage
    Conclusion.
    *1 .No apartment is a cottage
    *2 Some buildings being apartment is a possibility.
    Conclusion..
    *1Some cottages being apartment is a possibility.
    *2. No cottage is hut.
    Please explain.

  11. Sri says:

    Jahnavi Ji,

    In this case we must go with venn diagram process

  12. Anu says:

    1.
    A) ALL BIRDS ARE CATS
    B) SOME CATS ARE CRAZY
    C) SOME DOGS ARE BIRDS
    D) BIRDS ARE CRAZY
    2. Which of these FORM pair so that the conclusion can be derived from them?
    1) AB 2) BC 3)CD 4)AD

  13. Karan says:

    Hi Jahnavi, if you by venn-diagram.

    Then u can find ur answer.

  14. Shilpa says:

    if UP+PP gives no conclusion
    then how all+some=some is possible
    it should be all+some=no conlusion
    plz rply…

  15. Shilpa says:

    most teachers are boys.some boys are students.answer is some students are boys.
    can u explain me how
    cz its some+some or particular +particular which leads to no conclusion

    • karthik says:

      look at the sentence
      some boys are students=PP
      PP–>PP
      hence
      boys=A,students=B
      A to B —>B to A
      some students are boys
      most teachers are boys –i think its a PP
      so PP cannot mingle with PP that is PP–PP=no conclusion
      so u can avoid that sentence and check with the conclusions
      hope it helps u..

  16. Shilpa says:

    all bags are cakes .
    all lamps are cakes.
    conclu:some lamps are bags
    no lamp is bag.
    what will b the answer and how

  17. Shilpa says:

    all fishes are grey in color.some fishes are heavy should give no conclusion since its all+some but the answer is given all heavy fishes are grey in color…is it right???

  18. Shilpa says:

    all jungles are tigers.some tigers are horses.
    conclusions:
    some horses are jungle .
    no horse is jungle
    answer given is: Either a or b follows
    is it right?n how?

  19. Sandy says:

    thanks very helpful… :)

  20. THOMAS LIVIMBO says:

    THANKS FOR YOUR EASIEST WAYS IN DEALING WITH SYLLOGISM

  21. SEO says:

    I think this is one of the most important info for me.
    And i’m glad reading your article. But should remark on some general things, The
    web site style is perfect, the articles is really great : D.
    Good job, cheers

  22. Amish says:

    If example is : All cats are dogs . All cows are dogs.
    Answer is : No conclusion.
    How to explain this on above rules ?

    • Nikhil says:

      All cats are dogs
      All cows are dogs -> Some Cows are dogs ->Some dogs are cows.
      So , Now,
      All cats are dogs + Some dogs are cows = No Conclusion …..since All + Some = No Conclusion.

  23. Abhijeet says:

    Statements: All pens are books

    Some pencils are pens

    Conclusions: 1. some books are pencils

    2. Some pencils are books

    3. All pens are pencils

    4. None

    A.) 1 B.) 2
    C.) 3 D.) 4

  24. Abhijeet says:

    Can someone help me with the above question. The answer says only conclusion B) is right. Whereas in my opinion A) and B) both follows….kindly help!

  25. gee says:

    what exactly does some not reversed mean?

    • Nikhil says:

      Means… let , say ” No A’s are B’s + Some B’s are C’s = Some C’s are A’s”
      Details..
      Normal order for conclusion would have to be A->B then B->C = A->C so reversed would have to be “C->A”

  26. Avinash says:

    If some x are y then can we say that some x are not y?

  27. pari says:

    sir plz explain how to solve probability case k

  28. STATEMENT:
    SOME APPLES ARE FRUIT
    SOME FRUITS ARE SOUR
    CONCLUSION:
    SOME APPLES ARE SOUR
    SOME SOURS ARE FRUIT

  29. banks says:

    This article is good, however it needs some emphasis on the middle term distribution aspect. Article is incomplete.

  30. Soniya says:

    Thanks this is really very helpful.

  31. Soniya says:

    Thanks these rules are very important to solve problems.

  32. rohit says:

    hey guys help me with this and thank you for shortcuts
    a. All ambulances are life savers.
    b. No ambulances are bumper cars.
    1.No life savers are bumper cars
    2.No bumper cars are life savers
    3.Some life savers are no bumper cars
    4.None of the above

    • DAMU says:

      @rohit:: Only 3 Follows..
      EXP:: Rewrite 1st(a) statement as SOME LIFE SAVERS ARE AMBULANCES then apply (SOME +NO= SOME NOT ) rules ..

    • Nikhil says:

      Option 3 is the answer.
      Details….
      All ambulances are life savers -> Some ambulances are life savers -> Some life savers are ambulances + No ambulances are bumper cars = Some life savers are not bumper cars.

      i.e. uses the rule -> Some + No = Some not.
      Hope it helped.

  33. rohit says:

    all+some=no conclusion but in wiki(http://en.wikipedia.org/wiki/Syllogism) it says this
    All rabbits have fur. (MaP)
    Some pets are rabbits. (SiM)
    ∴ Some pets have fur. (SiP)

  34. ankit says:

    sir these type of que r easily solve by van diagram method but problem m there conclusion r in posibility so plz provided the short methed of it

  35. maithli says:

    how to solve this…this doesnot contains the words all,some,no..
    A. Grass eats lion
    B.lion eats mammal
    C.meat eats grass
    D.lion eats meat
    E.grass eats mammal
    F.lion eats grass

    options
    a) FDC
    b)DCF
    c)CBA
    d)FED

  36. Nikhil says:

    A very helpful , to the point post. Loved it. Keep up the great work!

  37. jenjen says:

    Stmt: I. All men are women. II. All women are girls
    Conc: 1. Some men are girls. 2. Some women are men.
    Ans: (a) 1 only (b) 2 only (c) both (d) either
    Whats the ans? Pls help.

  38. N Raju says:

    Thank u so much…its really very helpful
    thanks once again…

  39. N Raju says:

    Thank u so much its really very helpful…
    thank u once again

  40. N Raju says:

    Thank u so much…

  41. g.nareshkumar says:

    i want full material for syllogism plz any of u send it

  42. THOMAS LIVIMBO says:

    WHAT IS THE DIFFERENCE BETWEEN WHEN AND ONLY WHEN AND IF AND ONLY IF

  43. dipali says:

    Cn u explain me whn we use either or ?

    • rupesh says:

      suppose four statements are given in which 1st statement follows, 2nd, 3rd and 4th not followed now check the subject and predicate of the statements which are not followed, to fall under the category of either condition…
      1) the subject and the predicate of any two statement should be same.(note: if it satisfy the first condition then go for second condition)
      2) if the statement which have same subject and predicate are in the combination of (A+O) or (E+I) or (I+O) then that two statement will fall under either or condition ….

  44. Manjunath says:

    New pattern of syllogism

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s