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Question:

Each of the questions below starts with a few statements, followed by four conclusions numbered 1, 2, 3 and 4. You have to consider every given statement as true, even if it does not conform to the accepted facts. Read the conclusions carefully and then decide which of the conclusion(s) logically follow(s) from the given statements, disregarding commonly known facts.

Statements:

a. Some boys are scholars
b. Some teachers are boys
c. All scholars are observers

Conclusions:

1. Some scholars are boys
2. Some scholars are not boys
3. Some observers are boys
4. Some teachers are scholars

Explanation:

Some boys are scholars:

There are two possible deductions from this statement.

i) All scholars are boys (i.e. the set of scholars is a subset of boys)
ii) Some scholars are boys (i.e. the intersection of the sets of scholars and boys is not a null set)

Some teachers are boys

There are two possible deductions from this statement.
i) All boys are teachers (i.e. the set of boys is a subset of teachers)
ii) Some boys are teachers (i.e. the intersection of the sets of teachers and boys is not a null set)

All scholars are observers.

There are two possible deductions from this statement.
i) All observers are scholars (i.e. the set of observers and scholars are identical)
ii) Some observers are scholars (i.e. the set of observers is a subset of scholars)

Let us analyze the conclusions:

1) Some scholars are boys.This is true for both the cases that have been mentioned above,
2) Some scholars are not boysThis may or may not be true because there are chances that all scholars may also be boys.
3) Some observers are boys.We know that either all or some observers are scholars (i.e. the set of observers is definitely a subset of the set of scholars) and the intersection of the sets of scholars and boys is not a null set. This means that some observers will always be boys. Hence conclusion 3 is true.
4) Some teachers are scholars.The intersection of set of boys and scholars is not a null set and the intersection of set of boys and teachers is not a null set. But this doesn’t mean that the intersection of boys and teachers will also be a null set. There may or may not be some teachers who are scholars.
Thus this statement is incorrect.

Hence, option (a).

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