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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