Question : Directions: Three statements are given followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
1. All teachers are students.
2. All principals are teachers.
3. Some principals are doctors.
Conclusions:
I. Some students are teachers.
II. No student is a doctor.
III. Some students are principals.
Option 1: Only conclusions II and III follow
Option 2: All of the conclusions follow
Option 3: Only conclusions I and II follow
Option 4: Only conclusions I and III follow
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Correct Answer: Only conclusions I and III follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some students are teachers – From the Venn diagram, the circle of the teacher is completely inside the circle of the student. Therefore, this conclusion is true.
Conclusion (II):
No student is a doctor – From the Venn diagram, there is no negative relation between student and doctor. Therefore, this conclusion is false.
Conclusion (III):
Some students are principals – From the Venn diagram, the circle of principals is completely inside the circle of students. Therefore, this conclusion is true.
So, only conclusions I and III follow. Hence, the fourth option is correct.
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