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:
Some teachers are scientists.
All scientists are doctors.
All doctors are engineers.
Conclusions:
I. Some doctors are teachers.
II. Some engineers are teachers.
III. Some doctors are scientists.
Option 1: Only conclusions II and III follow
Option 2: Only conclusions I and III follow
Option 3: All conclusions follow
Option 4: Only conclusions I and II follow
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Correct Answer: All conclusions follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion I:
Some doctors are teachers – From the above diagram, it can be seen that the circle of doctors and teachers intersects and has some common area between them, which implies that some doctors are teachers. So, this conclusion is true based on the given statements.
Conclusion II:
Some engineers are teachers – From the above diagram, it can be seen that the circle of engineers and teachers intersects and has some common area between them which implies that some engineers are teachers. So, this conclusion is true based on the given statements.
Conclusion III:
Some doctors are scientists – From the above diagram, it can be seen that the circle of scientists is inside the circle of doctors, which implies that all the scientists are doctors and some of the doctors are scientists. So, this conclusion is true based on the given statements.
So, all the conclusions follow according to the given statements. Hence, the third option is correct.
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