Syllogism by Rules Part 6: Certain Controversy and Exceptional Case

Shortcut to solve syllogism by rules

Day 6: Certain Controversy and Exceptional Case

 

Two Exceptional Case of SOME NOT

On Day 3 we learned a rule that SOME NOT + ANYTHING = NO CONCLUSION
Here we will see two exceptional cases in which SOME NOT and ALL are involved. Rest everything can be solved by using the table discussed on Day 3.

Exception 1:

Exception 2:

In Rest All case of SOME NOT + ALL or Any other proposition we will get NO CONCLUSION

Example 1: Some A are not B + All B is C. Here the common term B is neither in the starting in both the proposition neither at the end in both proposition. So exceptional case is not valid here.

Example 2: Tell which of the following conclusion follows
Statement:
All red is pink
Some red is not green
Conclusion:
I. Some green are not pink
II. Some Pink are not green

View Answer

Explanation
: Only II. Follows
This is the case 1 of exception. Common term is in the starting. So arrange them in the order Some Not + All . Then take the term from down to up, as explained. We get Some Pink are Not Green

Example 3: Tell which of the following conclusion follows
Statement:
Some blue are not green
All red is green
Conclusion:
I. Some blue are not red
II. Some red are not blue.

View Answer

Explanation
: Only I. Follows
This is the case 2 of exception as the common term is at the end. So take the sentence in order All+ Some Not. Start from down move to Up as in the image of example 8. Some blue are not red

 

Certain Controversy

Case Solution
1 Does restatement follows? As explained on Day 5 The Rule is
1) Restatement Follows
2) Possibility of Restatement 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)
2. Does Some A is B means Some A are Not B or vice versa? NO. It does not means.
3. Does All + No makes complimentary pair? NO. They don’t. On Day 5 we have covered this topic
4. The statement
All A are Not B ???
What does it means
This is a controversial statement which can have two meaning. So you will never get this statement in exam.

Certain Special words used in Syllogism and their meaning

Terms Meaning Example
Atleast, Most, Many, few SOME Atleast some A are B*
OR
Most A are B
OR
Many A are B
OR
Few A are B
=> Some A are B
*In exams you will mostly find the case of Atleast.
Only Statement: Only A is B Conclusion: All B is A

Trick to solve the new pattern syllogism in short time using rules

By using rules we can solve the new pattern reverse syllogism questions in very less time. We can further reduce this time by having a correct thought process while solving the question. In the below example we will show the right approach to solve such question.

Example 4: Conclusions: Some cars are not trucks. Some buses are trucks.
STATEMENTS:
A) All cars are scooters. No bus is scooter. Some busses are trucks.
B) All cars are scooters. No truck is scooter. All trucks are busses.
C) All cars are scooters. All bus are scooters. All trucks are busses.
D) Some cars are scooters. No truck is scooter. No bus is car.
E) None

View Answer
  Option B

Now how to tackle such questions? You can either check all the option and get the correct answer easily. Or you can simultaneously use elimination and reduce the number of options that you have to check. To eliminate wrong options follow this approach:

One of the Conclusion is SOME NOT : When do we get SOME NOT? We get one SOME NOT when one of the proposition is SOME and another is NO. OR we can also get SOME NOT when tthere is case of NO :example No A is B also means that Some A is Not B. So even If All + No is there we can get SOME NOT.
So check in each option at a glance which option does not contains Some + No OR All + No together And eliminate that option as that cannot be the answer.
So we get Option C) cannot be the ans as it has Only ALL.

Now go to the second conclusion: We have the case of SOME. When do we get SOME? We get Some when the first proposition is Some and the second is All. Or both is ALL. Now scan the remaining options which does not have either Some+ All or All  + All together. So see that Option D is also eliminated.

Now we are left with only Option A) and B) now use the rules and check both the case. And get the final answer. You can practice this though process now and gain expertise over it  and use it in real exam.

Questions for Practise

  1. Conclusions:
    (i) All red is blue is a possibility.
    (ii) All green being yellow is a possibility.
    STATEMENTS:
    A) All red is yellow. All yellow is blue. No blue is green.
    B) Some red is yellow. No yellow is blue. Some blue is green.
    C) Some red is yellow. Some yellow is blue. No blue is green.
    D) All red is yellow. No yellow is blue. All blue is green.
    E) None
    View Answer
     Option C

    From option C, i) Some+Some = NO CONCLUSION and NO Conclusion means Any Possibility is True. => ) Some red is yellow. Some yellow is blue. = All red is blue is a possibility is true. AND ii) Some + No = Some Not => Some yellow is blue. No blue is green.= Some Yellow are Not Green => All green being yellow is a possibility. [Remember When SOME A is NOT B is true then All B being A is a possibility is also true.]
  2. Conclusions:
    (i) Some business are express
    (ii) Some express are times
    STATEMENTS:
    A) All business are standard. All standard is times. Some times are express.
    B) All business is standard. Some standard are times. All times are express.
    C) No business is standard. All standard are times. Some times are express.
    D) Some business is standard. All standard is times. No times is express
    E) None
    View Answer
     Option E

    Statement i) doesnot follow in any of the Option
  3. Conclusions:
    (i) Some heater are lamp.
    (ii) Some fan are lamp.
    STATEMENTS:
    A) All lamp are bulb. All bulb are fan. Some fan are heater.
    B) All lamp are bulb. Some bulb are fan. All fan are heater.
    C) Some lamp are bulb. All bulb are fan. All fan are heater
    D) All lamp are bulb. All bulb are fan. Some fan are heater.
    E) None
    View Answer
     Option C

    From option C, i) Some+All+All= Some => Some lamp are bulb. All bulb are fan. All fan are heater= Some lamp are heater= some heater are lamp(reverse) AND ii) Some +All=Some => Some lamp are bulb. All bulb are fan. = Some lamp are fan= some fan are lamp(reverse)
  4. Conclusions:
    (i) Some tulip are not lily.
    (ii) Some flower are rose.
    STATEMENTS:
    A) Some rose are not lily. All rose are tulip. All tulip are flower.
    B) All tulip are rose. Some lily are not rose. Some tulip are flower.
    C) All rose are lily. No lily is tulip. No tulip are flower.
    D) Some rose are lily. No lily is tulip. Some tulip are flower
    E) None
    View Answer
     Option A

    From Option A, i) ) Some rose are not lily. All rose are tulip.=> Some tulip are not lily AND ii) All+All = All => All rose are tulip. All tulip are flower.= All rose are flower= Some flower are rose.
  5. Conclusions:
    (i) All water being river is a possibility
    (ii) Some ocean are not lake.
    STATEMENTS:
    A) Some lakes are water. All water us ocean. No ocean is river.
    B) All lakes are water. All water is ocean. Some ocean is river.
    C) All lakes are water. No water is ocean. Some ocean is river.
    D) Some lakes are water. Some water is ocean. All ocean is river.
    E) None
    View Answer
     Option C

    From option C, i) No+Some = Some not reversed=> No water is ocean. Some ocean is river.= Some river are not water. = All water being river is a possibility. AND ii) All+ No = No => All lakes are water. No water is ocean. No Lake is ocean and hence Some Ocean are not lake is also true.

This is the end of the course in Syllogism by Rules. 

Ask your doubt in comment section.

Thank You!!!!!

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