Thursday, April 28

Syllogism

Rule 1 : All + All = All

Problem I
Statement 1 : All boys are intelligent
Statement 2 : All intelligent are girls

Therefor the conclusion derived will be
All boys are girls
From statement 1 : Some intelligent are boys
From statement 2 : Some girls are intelligent

Problem II
Statement 1: All books are pens
Statement 2 : All pens are pencils

I : All books are pencils
II : All pencils are books

From Rule 1 we can derive that All books are pencils
Hence, only conclusion I is true.

Rule 2 : All + No => No
When predicate of 1st statement is equal to Subject of 2nd statement

Problem 1
Statement 1 : All tigers are horses
Subject is "Tiger" and Predicate is "Horse"

Statement 2 : No horse is dog
Subject is "Horse" and Predicate is "Dog"

Since Predicate of 1st statement is same as subject of 2nd Statement, we can apply the rule.

I : No Tiger is Dog
II : Some tigers are dog

Therefore, as per Rule 2, the conclusion would be
No Tiger is Dog

Hence, only conclusion I is correct. Conclusion II cannot be correct.

 Problem II
Statement 1: All students are scouts.
Statement 2 : No Scout is Lady.

I : No Student is lady
II :  Some scouts are students

Therefore the conclusion after applying Rule 2 is
No Student is lady

From statement 1 : All Students are scouts, we can conclude that Some scouts are Students.

Therefore, we can conclude that both the given conclusions are true.

Rule 3 : All + Some => No Conclusion

Problem I
Statement 1 : All pens are pencils
Statement 2 : Some pencils are papers

I : Some papers are pens
II : Some pens are not papers

From Rule 3 : We can concur that there is No Conclusion. Note that for Rule to be used, Predicate of Statement 1 should be same as Subject of Statement 2.


Problem II
Statement 1 : All bats are balls
Statement 2 : Some balls are nets

I : Some bats are nets
II : All nets are bats

Applying Rule 3, There is No Conclusion

Rule 4 : Some + All => Some
In this scenario, there will be 2 conclusions.

Problem I
Statement 1 : Some parrots are Doves
Statement 2 : All Doves are Peacocks

I : All peacocks are doves
II : Some peacocks are parrots

Applying Rule 4, we get two statements
Some Parrots are Peacocks
Some Peacocks are Parrots

From 2nd statement "All Doves are Peacocks" we can derive that "Some Peacocks are Doves"

There the 2nd conclusion alone is true.

Problem II
Statement 1 : Some books are pens
Statement 2 : All pens are papers

I : Some books are papers
II : Some papers are books

Applying Rule 4 i.e Some + All => Some, we get
Some books are papers
Some Papers are books

Therefore both the Conclusion are true.

Rule 5 : Some + No => Some Not 

Problem I
Statement 1 : Some Books are Toys
Statement 2 : No Toy is Red

I : Some books are red
II : Some books are not red

From Rule 5 : Some books are not red.
From statement 1 : Some Toys are Books
From Statement 2 : No Red is Toy.


Problem II
Statement 1 : Some trains are trees
Statement 2 : No Tree is a Picture

I : Some trains are picture
II : No train is a picture

From Rule 5 : Some Train is not Picture
From Statement 1 : Some trees are Trains
From Statement 2 : No Picture is Tree

From above derivation, we can say that no conclusion is true.

Rule 6 : Some + Some => No Conclusion

Problem I
Statement 1 : Some stones are cups
Statement 2 : Some cups are black

I : Some blacks are not cups
II : Some cups are Stones

As per Rule 6 -> There is no Conclusion

Problem II
Statement 1 : Some dogs are rats
Statement 2 : Some rats are horses

I : Some horses are dogs
II : No horse is a rat

As per Rule 6 -> No Conclusion.


Rule 7 : No + No => No Conclusion

Rule 8 : No + All/Some => Some Not Reversed

Problem I
Statement 1 : No File is an Elephant
Statement 2 : All elephants are Caps

I : Some Caps are elephants
II : Some Caps are not Files

As per Rule 8 :
Some Caps are not Files
From Statement 2 we can derive -> Some caps are elephants

Therefore, both the conclusion are correct

Problem II
Statement 1 : No Goat is Door
Statement 2 : All doors are chairs

I : Some chairs are doors
II : Some chairs are goats
III : Some chairs are not goats
IV : Some doors are goats

As per Rule 8:
Some chairs are not Goats

From Statement 2
Some Chairs are Doors
Also -> Some Doors are Chairs (From above derivation)

From statement 1
No Door is Goat

Therefore I and III are true



Problem with 3 statements

Statement 1 : Some newspapers are radios
Statement 2 : Some radios are Television
Statement 3 : No television is magazine

I : No newspaper is magazine
II : No Radio is magazine
III: Some radios are not magazines
IV : Some newspapers are televisions


Statement 1 : Some newspapers are radios
We can derive -> Some Radios are Newspapers

Statement 2 : Some radios are Television
We can derivie -> Some Television are Radios

Statement 3 : No television is magazine
We can derive -> No Magazine is Television

From Statement 1 and Statement 2, we cannot derive any conclusion
From statement 2 and statement 3 : We can get -> Some Radios are not magazine

Therefore only III is true.

Problem with 3 statements

Statement 1 : All fowls are kites
Statement 2: No kite is insect
Statement 3 : No fowl is kite

I : No Fowl is insect
II: No Insect is Fowl
III : Some Kites are Fowls
IV : No Kite is Fowl

Statement 1 : All fowls are kites
=> Some kites are Fowls
     => Some Fowls are Kites

Statement 2: No kite is insect
=> No Insect is Kite

Statement 3 : No fowl is kite
=> No Kite is Fowl

From Statement 1 and Statement 2
No Fowls are Insects
=> No Insects are Fowls

Therefore from all the derived statements, we can get the result that all the conclusions are True.


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