Question : Directions: In the following question, two statements are given followed by two or four conclusions, I, II, III and IV. You have to consider the statements to be true, even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions can be drawn from the given statements. Indicate your answer. Statements: All aeroplanes are trains. Some trains are chairs. Conclusions: I. Some aeroplanes are chairs. II. Some chairs are aeroplanes. III. Some chairs are trains. IV. Some trains are aeroplanes.
Option 1: Only conclusions I and II follow
Option 2: Only conclusions II and III follow
Option 3: Only conclusions III and IV follow
Option 4: None follows
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Correct Answer: Only conclusions III and IV follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): Some aeroplanes are chairs – From the Venn diagram, it is evident that there is no direct relation between aeroplanes and chairs. So, no definite relation can be drawn. Thus, this conclusion does not follow. Conclusion (II): Some chairs are aeroplanes – From the Venn diagram, it is evident that there is no direct relation between aeroplanes and chairs. So, no definite relation can be drawn. Thus, this conclusion does not follow. Conclusion (III): Some chairs are trains – From the Venn diagram, it is evident that two circles representing chairs and trains overlap each other and have a part of their area in common. So, from this, it can be concluded that some chairs are trains. Thus, this conclusion follows. Conclusion(IV): Some trains are aeroplanes – From the Venn diagram, it is evident that some parts of the circle representing the train lie inside the circle representing the aeroplane while some lie outside. So, from this, it can be concluded that some trains are aeroplanes. Thus, this conclusion follows.
So, only conclusions III and IV follow. Hence, the third option is correct.
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