Shortcut to solve syllogism by rules

Day 3: Actual Rules Syllogism

Rule Table: Learn it so that next time you don’t have to refer this table

Note that we will have to use the concept of Rearrangement and Reversal that we have learned on Day 1 and Day 2 to solve Syllogism by rules.

Examples

1) All+All=All

All Red are Green + All Green are Blue. => Conclusion=  All Red is Blue
Note: The reverse of the obtained conclusion i.e Reverse of All Red is Blue = Some Blue is Red will also be true.

2) All + No= No

All Red is green + No Green is Blue => Conclusion= No Red is blue.
Reverse conclusion= No Blue is Red

3) All+Some=No Conclusion

All Red is Green + Some Green is Blue => Conclusion= No conclusion can be drawn between Red And Blue. (But No conclusion means that any possibility between Red and Blue will be true)
Example: All Red being blue is a possibility.
Some Red are blue is a possibility
Some red are not blue is a possibility
No red is blue is a possibility.
All these possibility are true.

4) Some + All= Some 
Some Red is green + All green is blue. => Conclusion= Some Red is blue.
Reverse conclusion=some blue is red.

5) Some + No = Some Not

Some Red is green + No green is blue=> Conclusion= Some Red is Not Blue

6) Some + Some= No Conclusion

Some Red is Green + Some Green is blue. => Conclusion= No Conclusion = Any possibility between Red and Blue is true (Same as in (3))

7) No + All = Some Not Reversed
No Red is Green + All Green is blue => (Apply Some Not on Reversed entity. i.e reverse Red and blue)
Means First Blue then Red at last and put Some Not
=> Conclusion= Some Blue are Not Red

8) No + Some = Some Not Reversed
No Red is Green + Some Green is blue => Conclusion= Some Blue is not Red

9) No + No = No
No Red is Green + No Green is blue => No Conclusion.

Exercise for the Day

Solve only by rules. Don’t use venn diagram.

1. Statement:
   (a) Some A are B
   (b) All A are C
   Conclusion:
   (i) Some B are C
   (ii) Some C are A
   (iii) Some B are A
   A) Only (i)
   B) Only (ii)
   C) Both (i) and (ii)
   D) Both (ii) and (iii)
   E) All
   
   View Answer

   Option E
   Explanation: For (i) => reverse(a) + (b) => Some B are A+ All A are C => Some + All= Some => Some B are C is true.
   For (ii) true by reverse of (b) . For (iii) True by reverse of (a)
2. Statement:
   (a) No pink is white
   (b) All white is red
   Conclusion:
   (i) Some red are not pink
   (ii) Some pink are not red
   A) Only (i)
   B) Only (ii)
   C) Either
   D) Both
   E) Neither
   
   View Answer

   Option A
   Explanation: No+All = Some not reversed=> Some red are not pink.
   Please Note: Some A are not B DOESNOT MEANS THAT Some B are Not A.
3. Statement:
   (a) All A are B.
   (b) Some C are B
   Conclusion:
   (i) All A are C
   (ii) Some A are C
   (iii) All A are C is a possibility
   A) Only (i)
   B) Only (ii)
   C) Only (iii)
   D) None follows
   
   View Answer

   Option C
   Explanation: For FIRST & LAST RULE to be applicable. We have to reverse (b). So we get
   All A are B + Some B are C => All+ Some = No conclusion between A and C => any possibility between A and C is true. So only (iii) is true.
4. Statement:
   (a)Some Samsung are Phone
   (b) No Samsung is Vivo.
   Conclusion:
   (i) Some Vivo are not phone
   (ii) Some Phone are not Vivo
   (iii) No Vivo is samsung
   A) (i) and (iii)
   B) (iii)
   C) (ii) and (iii)
   D) (ii)
   E) All
   
   View Answer

   Option C
   Explanation: For (ii): Reverse any of the two statement, as the preference of both are equal. Here I am reversing (a). So we get=> Some Phone are Samsung + No samsung is vivo => Some + No = Some Not => Some phone are not vivo. So (ii) is true. You can try by reversing (b). The conclusion will be same.
   For (iii) It is the reverse of (b). So true
5. Statement:
   (a) Some A are B
   (b) Some B are C
   Conclusion:
   (i) Some A are C
   (ii) No A is C is a possiblity
   (iii) Some C are B
   A) Only (ii)
   B) Only (iii)
   C) Only (i)
   D) None
   E) Both (ii) and (iii)
   
   View Answer

   Option E
   Explanation: For (ii) we have Some + Some = No conclusion between A and C. So any possibility is true between A and C. So (ii) is true.
   (iii) is true by reverse of (b)

Topic for Day 4: Use of rules to solve more than 2 statements simultaneously.

Ask your doubt in comment section.

Thank You!!!!!