Question : Directions: Two 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:
All teachers are engineers.
All clerks are teachers.
Conclusions:
I. Some engineers are clerks.
II. Some teachers are clerks.
III. Some clerks are not engineers.
Option 1: Only conclusions I and III follow
Option 2: Only conclusions I and II follow
Option 3: All of the conclusions follow
Option 4: Only conclusions II and III follow
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Correct Answer: Only conclusions I and II follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some engineers are clerks – From the Venn diagram, the circle of clerks is completely inside the circle of engineers. Therefore, this conclusion is true.
Conclusion (II):
Some teachers are clerks – From the Venn diagram, the circle of clerks is completely inside the circle of teachers. Therefore, this conclusion is true.
Conclusion (III):
Some clerks are not engineers – From the Venn diagram, there is no negative relation between clerks and engineers. Therefore, this conclusion is false.
So, only conclusions I and II follow. Hence, the second option is correct.
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