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Directions: In each question some statements followed by some conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follows from the given statements.
1
Statements:
No apple is a plum.
All plums are oranges.
All oranges are mangoes.

Conclusions:
I.  All plums are mangoes.
II. At least some mangoes are oranges.
» Explain it
D
Statements:
No apple is a plum.
All plums are oranges.
All oranges are mangoes.

Conclusions:
I.  All plums are mangoes.
II.  At least some mangoes are oranges.
 

All plums are oranges (A) + All oranges are mangoes (A) = A + A = All plums are mangoes. Hence, conclusion I follows.

All oranges are mangoes – converse – Some mangoes are oranges. Hence, conclusion II follows.

Hence option D is correct.
 
2
Statements:
All animals are mammals.
No mammal is reptile.
All reptiles are amphibians.

Conclusions:
I.  All animals are amphibians.
II. Some amphibians are mammals.
» Explain it
A
Statements:
All animals are mammals.
No mammal is reptile.
All reptiles are amphibians.

Conclusions:
I.  All animals are amphibians.
II. Some amphibians are mammals.
 
Checking  C1: All animals are amphibians.

The class 'animals' is in Statement 1 and 'amphibians' is in Statement 3 and the link or middle term is available in Statement 2 which is an E type statement. Clearly, using these we can't have an A type conclusion. C1, clearly, doesn't follow.

Checking  C2: Some amphibians are mammals.

Applying the same logic, we can't get a positive conclusion using Statement 2 and Statement 3. C2, doesn't follow either.

Option A is hence the correct answer.
3
Statement:
Some schools are classes.
Some classes are teachers.
All teachers are students.

Conclusions:
I.  Some students are classes.
II. All schools being students is a possibility.
» Explain it
D
Statement:
Some schools are classes.
Some classes are teachers.
All teachers are students.

Conclusions:
I.  Some students are classes.
II. All schools being students is a possibility.
 
 
Checking C1: Some students are classes.

Some classes are teachers + All teachers are students = Some classes are students. Clearly, C1 follows.

Checking C1: All schools being students is a possibility. 

Here, no negative statement is given among the statements. Clearly, possibilities between classes do exist. C2 follows as well.

Option D is hence the correct answer.

 
4
Statements:
Some buses are cars.
No car is ship.
All ships are bikes.

Conclusions:
I.  Some buses are not bikes.
II. No bike is ship.
» Explain it
A
Statements:
Some buses are cars.
No car is ship.
All ships are bikes.

Conclusions:
I.  Some buses are not bikes.
II. No bike is ship.
 
Checking C1: Some buses are not bikes.

Here, S1 is I type, S2 is E type, and the class 'bikes' is the predicate in S2 which is an A type statement. When we move from S1 to S2, we get a conclusion in O type statement and as we know O type doesn't make a definite conclusion applying deduction method. No definite conclusion can be derived out of S1, S2 and S3 together. C1, hence, doesn't follow.

Checking C2: No bike is ship.
 
Converse of S3 = Some bikes are ship. Clearly, C2 doesn't follow either.

Option A is hence the correct answer.
 
5
Statements:
All cups are saucers.
All plates are cups.
Some saucers are spoons.

Conclusions:
I.  All plates being spoons is a possibility.
II. All plates are not saucers.
» Explain it
B
Statements:
All cups are saucers.
All plates are cups.
Some saucers are spoons.

Conclusions:
I.  All plates being spoons is a possibility.
II. All plates are not saucers.
 
Checking C1: All plates being spoons is a possibility.

As there is no negative statement, possibilities between classes do exist. Clearly, C1 follows.

Checking C2: All plates are not saucers.


As there is no negative statement, a negative definite conclusion is not possible. C2, hence, doesn't follow.

Option B is hence the correct answer.