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 I and II follow
Option 2: All conclusions follow
Option 3: Only conclusions I and III follow
Option 4: Only conclusions II and III 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 Venn diagram, it is evident that the circles representing teachers and doctors overlap and have a part of their areas in common. So, from this, it can be concluded that some doctors are teachers. Thus, this conclusion follows.
Conclusion II:
Some engineers are teachers – From the Venn diagram, it is evident that the circles representing teachers and engineers overlap and have a part of their areas in common. So, from this, it can be concluded that some engineers are teachers. Thus, this conclusion follows.
Conclusion III:
Some doctors are scientists – From the Venn diagram, it is evident that some parts of the circle representing doctors lie inside the circle representing scientists while some lie outside. So, from this, it can be concluded that some doctors are scientists. Thus, this conclusion follows.
Therefore, all conclusions follow. Hence, the second option is correct.
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