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

In Aptitude by Support Staff

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

Question-Statements

Conclusion-Statements

  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

Approach

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)
Univ.Negative
  1. All mangoes(B) are fruits(C)
Univ.Positive
  • 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/