Syllogism by Rules Part 5: Possibility Case and Condition of Complementary Pair

Shortcut to solve syllogism by rules

Day 5: All the cases of possibility and Condition of Complementary Pair (EITHER-OR)

We have already discussed the main concept of Possibility i.e The case of NO CONCLUSION. Now we will some more cases where Possibility will be true. We have presented the proposition with all possible outcomes. Learn them.

Before starting learn this as a RULE OF THUMB:
1) Restatement Follows
2) Possibility of Restatement or Definite Conclusion Doesn’t Follows

Example: Statement: Some A are B
Conclusion: Some A are B(Follows)
Some A are B is a possibility(Doesn’t Follows)

Statement: All A are B Conclusions
Some B are A
Some A are B
All B being A is a possibility
Some B are not A is a possibility

 

Statement: Some A are B Conclusions
Some B are A
All B being A is a possibility
All A being B is a possibility
Some A are not B is a possibility
Some B are not A is a possibility

 

Statement: No A are B Conclusions
No B is A
Some A are not B
Some B are not A

 

Statement: Some A are Not B Conclusions
All B being A is a possibility  (Very Important)
No A is B is a possibility
No B is A is a possibility
Some B are not A is a possibility
Some A are B is a possibility
Some B are A is a possibility

 

Case of Complementary Pair (EITHER-OR)

There are only three conditions for two propositions to be Complementary pair. But remember for two propositions to be complementary pair, both of them must be False.

Case Example
Condition 1 Some + Some Not Some A are B + Some A are not B
OR
Some B are A + Some A are not B
Condition 2 Some + No Some A is B + No A is B
OR
Some B is A + No A is B
Condition 3 All + Some Not All A is B + Some A are not B

Note: All A is B + Some B are not A (is not complementary pair)[Very Important]

Questions for Practise

  1. Statement: All radios are pencils
    Some pencils are files
    Conclusion: I. No radio is file
    II. Some files are radio
    A) Only I follows
    B) Only II follows
    C) Either I or II follows
    D) Neither I nor II follows
    E) Both I and II follows
    View Answer
    Option C
    Explanation
    : All + Some = No conclusion ; with means both I and Ii are false.
    But they satisfy the condition of Complimentary pair (Some + No) : So Either Or is the answer
  2. Statements: Some diggers are jokers
    All jokers are cute.
    Conclusion: Some diggers are cute.
    II. No diggers are cure.
    III. Some diggers are not cute
    IV. All diggers are cute.
    A) I and III follows
    B) Either II or IV follows
    C) II and either III or IV follows
    D) Either III or IV and I follows
    E) Either I or II and either III and IV follows
    View Answer
    Option D
    Explanation
    : Using the statements we get the conclusion: Some +All= Some=> Some diggers are cute. So I follows. While II, III and IV donot follow. But III and IV make complimentary pair.
  3. Statements: All cones are cylinders. Some cones are squares. No square is a rectangle.
    Conclusions:
    I. Atleast some cones being rectangle is a possibility.
    II. Some cylinders are cones.
    A) only I follows
    B) only II follows
    C) either I or II follows
    D) neither I nor II follow
    E) both I and II follow
    View Answer
      Option E
    Explanation
    :
    For I. Using second and third proposition : Some+ No= Some not=> Some Cone is not Rectangle. So SOme COne being rectanlge is a possibility
    For II. It is the reverse of All cone are cylinder. So true

This is the end of our main course. On the last day i.e tomorrow we will discuss two exceptional case of syllogism and certain controversy and practice a lot of questions including the new pattern reverse syllogism. Revise all the content of these 5 days and be in regular touch with Syllogism by rules. Once you get habituated, you can solve any difficult question easily that too in less time.

Topic for Day 6: Exceptional case of syllogism and certain controversy.

If you have any controversial doubt related to syllogism, comment it below, we will include that too in our post tomorrow.

Ask your doubt in comment section.

Thank You!!!!!

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40 Thoughts to “Syllogism by Rules Part 5: Possibility Case and Condition of Complementary Pair”

  1. K!nG Iz B!nG

    10x team????

  2. YUMN ZAIDI

    more examples deyna sir

    1. Suraj

      yes.. you can join us at 10 PM on our discussion page,, we will discuss more questions…

  3. ANUP SINGH

    sir restatement follow krta h but restatement with possibility word follow ni krta, ryt?

    1. Suraj

      yes right…

      All A are B will be true…
      Some B are A is the reverse of All A is B.. means Some B are A is true..(definite conclusion)
      Possibility of Restatement or Definite Conclusion Doesn’t Follows
      means Some B is A ki possibility false hogi

      1. Laughing tym its nitrous oxide

        SIR Case of Complementary Pair (EITHER-OR)
        NHI AYA SAMAJH

        1. Suraj

          jo table diya hai, usme ye samjhay hai ki kis kis case me complementary pair bante hi…

          now suppose a questions i sthere
          Statement: Some A is B . Some B is C

          Conclusion: I. ALL A is C
          II. Some A is Not C

          Now iska answer hoga,, either I or II.
          pehli condition either or ki ye hai ki dono statement jinko eother or k liye check krna hai, wo False hone chahye, isme I. and II. dono false hai..

          second condition is ki, wo table. Agar the entity same hai, i.e A A and CC dono sentence me,, aur us table k according, yato
          Some A is C , SOme A is not C
          SOme A is C + No A is C
          All A is C + SOme A is not C

          in teeno me se koi bhi ek format ho conclusion ka to wo either or ka case banega..
          is question me 3rd wala case hai.. so either or

          1. Laughing tym its nitrous oxide

            x² – 30(POWER 5/2)/√x = 0

          2. Suraj

            x^2 = [30^(5/2)]/x^(1/2)
            => x^(2+1/2)=30^(5/2)
            x^(3/2)=30^(5/2)
            x^3=30^5
            iske aage solve nhi hoga,, ho sakta hai kisi power k value wrong ho,, yato 5/2 ki jagah 3/2 hota, ya root x ki jagah x^3/2 to answer aata sedha sedha

          3. Laughing tym its nitrous oxide

            SOL YEH diya hai see
            x² – 30(pwr5/2)/√x = 0
            x(5/2) = 30(5/2)
            x = 30
            () wala power hai

          4. Suraj

            wrong diya hai ye to.. kyunki x k sath power 5/2 nhi 3/2 hi ayega.. 2+1/2(for root)

          5. Laughing tym its nitrous oxide

            ji and next dekhna sir

          6. Suraj

            ok kar diya dono

          7. Laughing tym its nitrous oxide

            360/y = 360/(y +5) + 1

          8. Laughing tym its nitrous oxide

            480/x = [480/(x – 8)] – 3

          9. PHENOMENAL

            Sir AGR diya ho some A is C and no C is A tb kya either or hoga?

  4. sachin shukla@Target sbi po

    sir some a are b then conclusion some a are not b is a possibility kaise sahi hoga?

    1. Suraj

      yes it is true,, doubt kaha hai?? means kyu true nhi ho sakta???

      1. sachin shukla@Target sbi po

        sir thoda details me smjha dijie ispe

        1. Shyam Veeri

          some a are not b is doubtful because it can’t be concluded from the statement definitely. And the possibility of doubtful case is always correct.

  5. Stoic

    @surajskt:disqus sir
    possibility me either-or follow krega?

    1. Suraj

      no, possibility me either-or follow nhi karega
      good question

  6. Bhatt Lalit

    Suraj could you please explain the below query using the method explained in your site…

    Statements:
    No key is door, All door are lock, Some window are key, Some door are window
    Conclusions:
    I. All window being door is a possibility
    II. All lock being key is a possibility
    III. No key is lock.
    IV. All lock are door
    1.Only I doesn’tfollows
    2.Only I and III follow
    3.Only I, III and IV doesn’t follow
    4.Only I, II and III doesn’t follow
    5.None follows

    What is the answer?

    1. I. Some Window are key + no key is door =>Some + No= Some Not=> Some window are not door (Hence all window being door is not possible). I false*
      II. No key is door, All door are lock, => No + All= Some not reversed => Some lock are not key (hence II is false)
      III. Same are II.
      IV. All door are lock=> Some lock are door=> IV. Is false

      Note*= For relation I. i.e between window and door; we can get relation between door and window using (Some Window are key + no key is door) together while using Some door are window alone. So in such case we must get the relation true in both cases. But here the relation is false by the (Some Window are key + no key is door) together. So it is false

      1. Bhatt Lalit

        Thanx buddy..?

      2. PHENOMENAL

        Thanx ma’am, one doubt when it is given Some A is not B what are the possibilities and conclusion? And if it is given a) Some A is B b) No B is C c) Some C is D , what can be the conclusion and possibilities?

  7. Kattula Kristu Raju

    sir please share some questions on reverse syllogism

  8. vinay

    Sir in dono ka ans n explanation bata dijiye plz
    https://uploads.disquscdn.com/images/60b https://uploads.disquscdn.com/images/6370a7507a14fca2d5f7404f38d23b563f946d6e805d40a11b274f26ee0400a9.jpg 66c6198c554ed06012d4d16ae305874b56b0b631df2ca425f1c0d5a84fb0f.jpg

  9. vinay

    Sir mere qsns ka ans nh diya apne??

    1. Learnie

      When you follow the rule method this one is easy and valid conversion too

  10. Ragul Kishore

    Some baskets are caskets.
    Some caskets are trunks.
    All trunks are fans.
    All sweets are fans.
    Conclusions:
    I. At least some baskets are trunks is a possibility.
    II. At least some fans are caskets is a possibility.
    III. All fans are baskets is a possibility.
    IV. At least some sweets are not caskets is a possibility.

    Does second conclusion follows ??

    1. ครђ

      Yes. II will follow

      As said Atleast some fans are caskets is a possibility. Means You have to take FANS as first element so do reverse of statement 3 …you will get All fans are trunks now look at sentence 2 .. trunks is at last so reversal of this statement will also require. make it Some Trunks are caskets Now you have :
      All fans are trunks Some Trunks are caskets All + some = No conclusion means Any possibilty is true 🙂

      1. Ragul Kishore

        Can we convert a all statement like that .. not we cannot convert it like that

  11. Ragul Kishore

    Sir , if we combine
    Some caskets are trunks.
    All trunks are fans.
    We get some casket are fans , then we know for sure some fans are casket , then how come some fans are casket is a possibility follows .

  12. Ragul Kishore

    @surajskt:disqus sir,

    Some baskets are caskets.
    Some caskets are trunks.
    All trunks are fans.
    All sweets are fans.
    Conclusions:
    I. At least some baskets are trunks is a possibility.
    II. At least some fans are caskets is a possibility.
    III. All fans are baskets is a possibility.
    IV. At least some sweets are not caskets is a possibility.

    Sir , if we combine
    Some caskets are trunks.
    All trunks are fans.
    We get some casket are fans , then we know for sure some fans are casket , then how come some fans are casket is a possibility follows

    1. ਹਰ੍ਸ਼ ਬਰਾੜ

      1 , 3 and 4 follows
      2 won’t follows

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