[Reasoning Q] 3-Statement Syllogism doubt Question: Apples, Mangoes, Vegetarians

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Mrunal's Economy Course

In an earlier article, we saw how to approach 3-statement syllogism (click ME)
One of the Reader “Pars”, had posted a doubt-question. Let’s solve it, to strengthen our grip over the UP-UN method.

  1. Question
  2. Solution and Approach
  3. i) No Fruit is apple
  4. ii) No vegetarian is apple
  5. Complimentary case example
  6. iii) some vegetarian are mangoes



  1. No Apple is mango
  2. All mangoes are fruits
  3. All fruits are vegetarians
  1. No Fruit is apple
  2. No vegetarian is apple
  3. some vegetarian are mangoes
  4. some vegetarian are Apple

Answers choices

  1. None follows
  2. All follows
  3. Either II or IV and III follows
  4. Either II or III and I follow
  5. none of these


Start checking answer statements one by one

i) No Fruit is apple

  • Q. if this is a valid conclusion, then who are its parents?
  • Ans. The parents are those statements having the words: fruit, apple and a common term.
  • First and second question statement meet this criteria
Statement Type
  1. No Apple(A) is mango(B)
  1. All mangoes(B) are fruits(C)
  • Three terms=Ofcourse yes.
  • Are they in standard format (A to B then B to C)? Yes.
  • Then what are you waiting for? Just apply the combo rules: UN+UP=??
  • 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). (UN+UP/PP=PN)
  • So conclusion has to be Some fruits(C) are not Apples (A).
  • Therefore, first given conclusion statement (No fruit is apple)=incorrect.

Move to next conclusion statement

ii) No vegetarian is apple

  • Q. if this is a valid conclusion, then who are its parents?
  • Ans. The parents are statements having the words:  vegetarian, apple and a common term
  • But there is a Problem: We cannot find two such statements directly.
  • Situation calls for Chain formula (A to B1, B1 to B2 and ultimately B2 to C)
Given question statements Type
  1. No Apple(A) is mango(B1)
Universal Negative (UN)
  1. All mangoes(B1) are fruits(B2)
Universal Positive (UP)
  1. All fruits(B2) are vegetarians(C)
Universal Positive (UP)

All of them are in standard format. So directly apply combo formulas.

  • First 1+2=> UN+UP= Particular Negative (C to A)
  • Therefore, 1+2= Some fruits(B2) are not apples.(A). (actually we already found this conclusion while solving conclusion statement (i) ^ in previous paragraph.)
  • Anyways, this is our intermediate conclusion.

Now combine this with third question statement

Statement type
Intermediate Some fruits(B2) are not apples.(A) PN
Third statement All fruits(B2) are vegetarians(C) UP
  • They are not in standard form.
  • PN statement cannot be converted.
  • So we’’ll convert UP statement.(**short cut is possible)
Intermediate Some fruits(B2) are not apples.(A) PN
Third statement Some vegetarians (C) are fruits(B2). UP–>PP converted.

Still not in standard format. Just exchange position of both statement.

Third statement Some vegetarians (C) are fruits(B2). PP
Intermediate Some fruits(B2) are not apples.(A) PN

Now they’re in standard format.
Apply combo rule: Two particular statement=no definite conclusion.

**please note: short cut was possible

  • Since given question statements: PN+UP were not in standard form. So definitely, we had to convert UP (because PN cannot be converted).
  • But you already know that UP converts to PP. Finally PN+PP =no conclusion. Therefore, whatever I’ve written ^above in green color font was just for explanation, otherwise no need to waste time in actually converting statements like ^that.

Hmm….now what to do?

Since the answer choices are in form of “either this or that..” we’ll now check if there is possibility for any complimentary case (in answer choices)?

Complimentary case example

When do we check for complimentary case?

Recall the standard operating procedure for 2-statement syllogism

  1. Two statements with three terms? Yes
  2. Question statements are given in standard format (A to B Then B to C). if not, then rearrange or convert them.
  3. Classify the statements (UP, UN, PP, PN)
  4. Apply the rules. Get the answer.
  5. If Step #4 gives “No conclusion” AND one of the answer choice is in the format of “Either I or II follows”, only then check for complementary case.

For complementary case to be valid, condition is= Two answer choices have same subject and predicate.

Answer choice combo example
  1. Uttar Pradesh (UP) + Pritish Nandy (PN)
1. All Politicians are honest.2. Some Politicians arenot honest
  1. PP + Pritish Nandy (PN)
1. Some Politicians are honest.2. Some Politicians arenot honest
  1. PP + United Nations (UN)
1. Some Politicians are honest.2. No Politicians are honest
  • Right now we are considering this answer choice ii) No vegetarian is apple (UN)
  • Another answer choice that matches it: iv) some vegetarian are Apple (PP)
  • So this answer choice combo like one of the complimentary answer choice case (PP + United Nations (UN).
  • Therefore either ii) or iv) is correct.

Move to next conclusion statement

iii) some vegetarian are mangoes

  • Q. if this is a valid conclusion, then who are its parents?
  • Ans. The parents are those statements having the words:  vegetarian, mangoes and a common term
Given question statements Type
2. All mangoes(A) are fruits(B) UP
3. All fruits(B) are vegetarians(C) UP
  • Are they in standard form? Yes. (A to B then B to C)
  • Apply combo rule: When Uttar Pradesh is merged with Uttar Pradesh, its size doesn’t increase.
  • UP+UP=UP (A to C)
  • Conclusion: All Mangoes(A) are vegetarians.(C) (UP)
  • Apply conversion rule: UP==>PP
  • Some Vegetarians (C) are Mangoes (A).
  • Therefore statement iii) is correct.
  • Ultimate answer: Either II or IV and III follows

Mr.Hakin has solved the same question with Venn-Diagram approach. Use this link to check it http://postimage.org/image/71zd7tvxz/

Indian History Freedom Struggle Pratik Nayak

98 Comments on “[Reasoning Q] 3-Statement Syllogism doubt Question: Apples, Mangoes, Vegetarians”

  1. Sir thanks for such a good explanation…
    Can you please suggest some reference(book or website) for IT specialist-II officer opening for 19 PSB’s…I will appear.

  2. Thanks for putting up this explanation and Hakin for venn-diagram approach…..

  3. Another problem looks easy but my answer did not match…

    Statements (A) All rackets are jackets
    (B) No cow is cat
    (C) Only cats are dog

    I some rackets are not cats
    II some cats are jacket
    III some rackets are cats
    IV no dog is a cow

    Answers (a) only either I or II and IV follow (b) only II and IV (c) only III and IV (d) only I and IV (e) none of these

    My approach
    First two statements have four items so there would be relation cat-racket or cat-jacket so first three are gone

    B and C are UN+UP= PN C—A conclusion some dogs are not cow

    so my answer is “e”………which is wrong

    Now what???????

    1. Pars,

      I got the answer as d) only I and IV follows

      Could you clarify whether it is the correct answer. If yes, then I would give the explanation else there is not point elaborating. :-)

      1. According to the book I am following …it is a wrong answer …..according to them the correct option is “a”….Now, one of the reader below is saying that the answer is wrong in the book……so confusion continues!!!!!!!!

        1. I think a is correct..

        2. actually u r right answer should none of these or
          either 1 or 3 (because complimentry pair)
          some books use ven diagram to solve it which many times gives answer opposite to syllogism rule


      2. Can u xplain how conclusion 1 follows ?

    2. Oops..mistaken..only four is right

    3. Can anyone please explain it ?

      1. only 4 is correct…………
        only cats are dog ……can be…all dogs are cats{UP}
        no cow is cat………..can be….no cat is cow{UN}
        No dog is cow

    4. (a) is correct…solve using venn diagram

      1. answer is D: how?
        one state ment is negtive and other is postive. and both are give false result so either i and iv is answer..

    5. either 1 or 3 should be correct answer because they form a complimentary pair, while other options are wrong.

    6. It’s definite 1st option

  4. coz answer given in that book is wrong… only 4 is correct……. in the book 1or 2 and 4 is correct is the answer

    1. only 4 is correct

  5. Q.Consider the following Statements:
    1. All countries are continents.
    2. Some Countries are oceans.
    3. No ocean is a Sea.
    4. All seas are continents.

    Which of the following inferences can be drawn from the above statements?
    A. Some seas are countries.
    B. All oceans are Continents.
    C. Some Oceans are continents.
    D. All countries are oceans.

    I have encountered this ques today in a mock test.
    I have done it through UP-UN method.
    while matching with the answer it doesnt match.
    I wanted to know the correct answer for the same as by doing it with the Venn method it seems to be easy and it matches with the answer too in this particular case.

    Please do the needful….!

    1. ‘A’ and ‘C’ follows. Is that correct?

    2. Only “C” is correct…….convert 2 into some ocean are country now combined it with statement 1…which is PP+UP=PP ..means “some ocean are continents”.
      B and D eliminated bcz you UP+UP to get these…
      A is eliminated bcz PP+UN=PN which will give “some country are not sea…..this is PN which cannot be converted to anything so we cannot say if “A” will be true…

      1. Option C is Correct…!

    3. B and C is the right ans

      please tell me if i am wrong then i will explain to you

  6. sorry, ans is definetely C

  7. Statement -all beer are wine.no wine is vodka.All vodka are rum.
    Conclusion- I.some rum are beer.
    II.Some rum are not beer.

    1. only 1 is true.
    2.only 2 is true.
    3. either conclusion 1 or 2 is true.
    4. neither conclusion 1 or 2 true.

    Mrunal ji answer it …1/2/3/4/5 .. :) (no need to explain your answer )

      1. neither conclusion is true

    1. 2 ….wat say mrunal

    2. yepp 2…. i read it other way round….some beer are not rum

    3. 3 is correct. Either or..for sure :D

      1. only 2 is true.. solve it again

        1. o yes!!!!!!!!!!! only 2 is correct!

  8. Hi Mrunal Sir,
    I found out this article of yours extremely useful.Can you please write a write-up on solving binary logic problems.
    To clarify myself in these question type three person speak two statements each-one of which is true and the other is false.Then we have to answer certain questions based upon these.
    Kindly look into this request.

    1. Yes mrunal sir..indeed they r pretty mind boggling..can’t be solved without help of a genius like you :)

  9. murnal sir please provide previous papers of assist labour commissioner of upsc and study plan for the exam ,recommed books .

  10. Consider the following statements:
    1. Some bills are duplicate.
    2. Some duplicate are original.
    3. All bills are original.
    4. No memo is duplicate.

    which of the following conclusions can drawn from the above statements?
    (a) Some memos are not duplicate
    (b) Some memos are bills
    (c) No original is bill
    (d) Some memos are original
    mrunal sir please tell me what is answer i am confused.
    please reply thanks

    1. I believe you have posted it from CL mock paper. I too have doubts with the answer. CL mentions that it should be A.
      But we know that UN can be converted to UN or PN in following two forms “no duplicate is memo(UN)” or “some duplicate are not memo(PN)”. But is the given PN form i.e. “Some memos are not duplicate” also valid.
      Can somebody please guide.
      Mrunal sir if you can look into this

      1. answer to this question shoul be [d] some memos are original.

  11. praween you are right this question from CL mock paper
    please help anybody thank you.

    1. acc to question we can not draw any conclusion from statement 1+3 and 2+3 as they are formin UP+ PP situation.
      so we left with UN+ PP situation in statement 4 with respect to 1 and 2……….this lead to PP+UN=PN ,and we lend to “some duplicate are not memo”.Fine this is a case like “some p are not q”.
      Their are two commonly made conclusion that are made wrong as follos……..
      some p are q.
      some q are not p.
      Hence from 2nd one …”Some memos are not duplicate” can not be answer at all.

      1. Matt
        Can you tell whether a direct conversion of UN to PN in the following form is permitted or not?
        UN:”no p are q” to PN:”some p are not q”
        (as per mrunal’s blog: “no q are p” and some q are not p” are valid)
        Kindly bear with me

        1. hi praween
          look to this….
          case:1 No P is Q
          This statement is the simplest and has just one interpretation…i.e P and Q are disjoint sets.
          Apart from this ,how could one establish a relation b/w P and Q.

          case:2 Some P are not Q
          This means there is at least one P which is not a Q.
          Plz heed on ATLEAST word.It is quite possible that no P may be Q.thus in this case some P are Q can not follow,it is one of the possibility.Similarly ”some Q are not P” is commonly wrong made conclusion…

          correct me if i am wrong

          1. Hi matt,

            I agree with you on case 2. But in case 1 according the write-up by Mrunal sir, two interpretations are possible.
            I have also mentioned those interpretations in my last post. So can you please elaborate more on this.
            And according to CL answer key the answer is A.

        2. hi praween ….acc to you what should be ans to this question.As i tried to solve it through vein diagram method and came to “d” option.

          1. Answer 1 hoga…. Sochna kya hay,,,, statement 4 se hi deduct ho jaega up pp np ki need NHi hay,,,,apply ur mind

  12. Mrunal sir …could you provide an article to solve the problems based on cause and effect relation,I have one such question………..
    Consider the following statements:
    1. Fringe operates only when supernatural shrieks.
    2.If baby reads supernatural shrieks.
    3.only if baby reads does the horizon improve.

    from the above four statements it may be concluded that:
    a. Horizon improves only if fringe operates
    b.each time supernatural shrieks horizon iproves
    c.baby reads only if fringe opertaes
    d.none of the above

    1. hi all, I’m kinda busy at the moment but i’ll deal with these syllogism questions and post the answer/explanation/approach in separate article in a few days.

      1. a big thank with pleasure to you sir………

      2. sir, Plz add few more types of possibility syllogism. Possibility is the new type of syllogism.

        1. In upcoming days, I’m writing 4 statement syllogism article, keeping the SBI PO type questions in mind.

    2. answer must b A .. Since statement 2 is connecting 1 and 3.. Nd option b and c cant be concluded by them.
      If u know the answer, can you plz tell if its A, B or C ?

        1. Pretty simple….horizon if n only if baby reads…now fringe can operate and supernatural can shriek even if baby doesn’t read as baby reading is not necessary condition for them

  13. Mrunal sir I understood this syllogism very well from articles provided by u but getting some problem in following type of questions Q- Statement A: All valid syllogism that distribute their middle terms in atleast one premise.
    B: This syllogism is a syllogism that distribute in atleast one premise.
    Conclusion I: This syllogism is a valid syllogism
    II: This syllogism is a syllogism with the middle term distributed.

    Which of the conclusion above is/are true?


    Q- Statement A: The only book in this library that i do not recommend for reading are unhealthy in tone.
    B: The bound books are all well written.
    C: All the romances are healthy in tone.
    D: I do not recommend that you read any of the unbound Books.

    Conclusion I: Therefore, all the romances in the library are bound books.
    II: Therefore, all the romances in the library are well written.

    Which of the conclusions above is/are correct?

    sir, please explain these questions.
    and thanks for all your efforts in providing us these valuable articles.

    1. such questions are tricky in nature…..
      answer for second question……None of the conclusion follows statement.
      for first question{syllogism}…..both of the conclusion follows.
      plz correct me if am wrong.

    2. Hi Rajeev, I solved through venn diagram and answers are correct.
      Q.1. Valid syllogism = middle term distributed + atleast 1 premise.
      Therefore, if only middle term distributed, it is a valid syllogism – cannot follow. It has to be middle term distributed AND in 1 premise. Middle term can be distributed in 1 or more than 1 premise.

      Q.2 Honestly, i didnt solve this through any method. Just plain english. But this method may not work always..
      All romances are bound books. Definitely not. Unbound books may be romance books as well.
      All romances are well written. No…They have never mentioned that.

  14. Hi matt,
    thanks for your try but answers are wrong
    1- a
    2- d
    can any one explain it

  15. a means only 1
    d means neither 1 nor 2

  16. sir
    i have a small doubt….
    statemnt:no cats are dogs

    valid conversions:1.no dogs are cats
    2.some dogs are not cats
    you said these two are valid conversions for the above statement….but
    why this is not possible….”some cats are not dogs”

  17. statements:1.all A are B
    2.some A are c

    conclusion:some B are C
    but you told that…..UP+PP=NO CONCLUSION

    1. please recheck your question statements, they’re not in standard format. (i.e. first term to middle term, the middle term to third term.) they must be converted into std. format first. even then it’d be PP+PP= two particulars = no conclusion.

      1. ya….i understood…..thank u mrunal…..

      2. Some A are C —-> can be converted to Some are C are A
        And now we have , Statement 1 : Some C are A —> PP
        Statement 2 : All A are B ——> UP

        So, the conlcusion should be Some C are B as PP+UP = PP right ?
        Sir, please correct me if Im wrong …..
        Thank you

  18. pls find the answer
    statement: a. some gases are liquids
    b. all liquids are water
    conclusion: 1. all gases being water is a possibility
    2. all such gases which are not water can never be liquids

    1. @Adi ..Both conclusions are correct

  19. @Adi ..Both conclusions are correct

    1. hi simran,

      can u plz elaborate abt the 1st conclusion & how to solve such qstns?

  20. For Conclusion 2 i’m getting separate answer:

    C2 -> No Veg is apple.

    1. No apple is mango
    2. All mango are fruits
    3. all fruit are veg.

    Taking 2 & 3 first instead of 1&2.

    All mango are fruits (UP)
    all fruit are veg (UP)
    UP + UP = UP which is “All mango are veg”

    Now taking 1 & above result

    No apple is mango (UN)
    All mango are veg (UP)
    UN + UP = PN (reversed) which is:
    “Some veg are not apple” (PN which cant be converted), but the conclusion 2 says “No veg is apple”.

    So conclusion 2 is false right.

    Please correct me if i am wrong

    1. either 2 or 4 has to be true. both cannot be false at the same time and we can’t say which one will be true because as per the question there can be different venn diagrams and we cant consider any one while answering the question. and with that conclusion 3 is true of course. Sorry for my next comment. I didnt see the question first.

  21. yes conclusion-2 is FALSE.

  22. just make the venn diag and whenever there is more then one case possible …then it cant be the answer .. the ultimate shortcut

  23. sir .urgent need plz solve the upsc csat 2012 syllogism question.i m not getting the question statement how to simplify it..
    ALL X brand cars parked here are white
    Some of them have radial tyres
    All X brand cars manufacture after 1986 have radial tyres.
    All cars are not branded

    Only white cars are parked here
    Some white X brand cars with radial tyres are parked here
    Cars other than X brand cannot have radial tyres
    Most of X brand car are manufactured before 1986

    1. I think only Some white X brand cars with radial tyres are parked here is TRUE. So, Only II is true.

  24. How this will be solved?

    1. all cats being dog is a possibility
    2. all dogs are tall

  25. @ santanu can u plz explain or plz simplify the statements

  26. mrunal sir plz need ur help in this question..

  27. Plz help solving this question of CSAT 2011;

    Directions to the question: Following question consists of 4 statements. Of these four statements, two cannot both be true, but both can be false. Study the statements carefully and identify the two that satisfy the above condition. Select the correct answer using the codes given below each set of statements.

    Ques: Examine the following statements:
    1. All animals are carnivorous.
    2. Some animals are not carnivorous.
    3. Animals are not carnivorous.
    4. Some animals are carnivorous.

    a) 1 and 3
    b) 1 and 2
    c) 2 and 3
    d) 3 and 4

    1. always go through …. all+ none option … u will find ur answer ….

      1. But why? Explain by mrunals method or his method can’t be applied in this ques?

  28. B. as per me both statements can be false by saying “no animals are canlrnivores”, but both statement cannot be true at the same time. Verify also by venn diagram, it will be more clear. Please correct me if i am wrong.

    1. b cant be bcoz aleast one animal is carnivorous

    2. but the answer is (a). How can it be solved by mrunal’s method.

  29. Mrunal Sir, Kindly solve this by your method, which I’m unable to:

    Some books are papers
    Some papers are desks
    Some desks are chairs

    I) Some books are desks
    II) Some papers are desks
    III) Some books are chairs

    1) None follows
    2) Only I follows
    3) Only II follows
    4) Only III follows
    5) Only I and II follow

  30. My doubt is a very basic one…
    When given

    ‘All cats are dogs.’ in the statement part
    can a conclusion

    ‘Some cats are dogs’ follow ???
    if yes plzz xplain.. i was taught so in my coaching class…

    1. yes that means both : 1)some cats are dogs and 2)some dogs are cats

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