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:
Some carpenters are singers.
All singers are doctors.
Conclusions:
I. No doctor is a carpenter.
II. Some doctors are singers.
III. Some carpenters are doctors.
Option 1: All of the conclusions follow
Option 2: Only conclusion II follows
Option 3: Only conclusion III follows
Option 4: Only conclusions II and III follow
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Correct Answer: Only conclusions II and III follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
No doctor is a carpenter – From the given Venn diagram, there is no negative relation between a doctor and a carpenter. Therefore, this conclusion is false.
Conclusion (II):
Some doctors are singers – From the given Venn diagram, the circle of singers is completely inside the circle of doctors. Therefore, this conclusion is true.
Conclusion (III):
Some carpenters are doctors – From the given Venn diagram, the circle of carpenters intersects the circle of doctors. Therefore, this conclusion is true.
So, only conclusions II and III follow. Hence, the fourth option is correct.
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