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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. All teachers are professors
b. All professors are researchers
c. All researchers are consultants

Conclusions:

1. Some consultants are teachers
2. All professors are consultants
3. Some researchers are teachers
4. All professors are teachers

Explanation:

All teachers are professors.

This means that either the set of teachers is identical to the set of professors or the set of teachers is a subset of the set of professors.

All professors are researchers.

This means that either the set of researchers is identical to the set of professors or the set of professors is a subset of the set of researchers.

All researchers are consultants.

This means that either the set of researchers is identical to the set of consultants or the set of researchers is a subset of the set of consultants.

Let us analyze the conclusions now

1) Some consultants are teachers
This is true as the set of teachers will atleast be a subset of professors which atleast will be a subset of researchers which will atleast be a subset of consultants.
2) All professors are consultants.
Set of professors will always be atleast a subset of researchers which will always be atleast a subset of consultants.
Hence this statement is also true.
3) Some researchers are teachers.
From the analysis of statement 1, we know that this statement is also true.
4) All professors are teachers.This is untrue because the set of professors is not a subset of teachers.

Hence, option (d).

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