Question : Directions: Consider the given statements to be true even if they seem to be at variance from commonly known facts and decide which of the given conclusions can definitely be drawn from the given statements. Statements: I. All astronomers are scientists. II. Some scientists are shopkeepers. Conclusions: I. All astronomers are shopkeepers. II. Some shopkeepers are astronomers. III. Some shopkeepers are scientists. IV. All scientists are astronomers.
Option 1: Only conclusion I follows
Option 2: Conclusions I, II, and III follow
Option 3: Only conclusion III follows
Option 4: Conclusions II and IV follow
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Correct Answer: Only conclusion III follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion I: All astronomers are shopkeepers – From the Venn diagram, it is evident that there is no direct relation between astronomers and shopkeepers. So, no definite relation can be drawn. Therefore, this conclusion does not follow. Conclusion II: Some shopkeepers are astronomers – From the Venn diagram, it is evident that there is no direct relation between astronomers and shopkeepers. So, no definite relation can be drawn. Therefore, this conclusion does not follow. Conclusion III: Some shopkeepers are scientists – From the Venn diagram, it is evident that the circles representing shopkeepers and scientists overlap each other and have a part of their areas in common. So, from this, it can be concluded that some shopkeepers are scientists. Therefore, this conclusion follows. Conclusion IV: All scientists are astronomers – From the Venn diagram, it is evident that some parts of the circle representing scientists lie outside the circle representing astronomers while some lie inside. So, from this, it can be concluded that some scientists are astronomers. Therefore, this conclusion does not follow.
Therefore, only conclusion III follows. Hence, the third option is correct.
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