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
S.No
First Proposition
Second Proposition
Conclusion
1
ALL
ALL
ALL
2
ALL
NO
NO
3
ALL
SOME
NO CONLCUSION*
4
SOME
ALL
SOME
5
SOME
NO
SOME NOT
6
SOME
SOME
NO CONCLUSION*
7
NO
ALL
SOME NOT REVERSED
8
NO
SOME
SOME NOT REVERSED
9
NO
NO
NO CONCLUSION*
10
Some Not
Anything(Some/No/All/Some Not)
NO CONLCUSION*
*No Conclusion= Any Possibility is True
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.
- 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
- 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
- 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
- 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
- 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)
Topic for Day 4: Use of rules to solve more than 2 statements simultaneously.
Ask your doubt in comment section.
Thank You!!!!!