Question : Directions: In this question, 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 follows/follow from the statements.
Statements:
Some roses are yellow.
Some yellow are buses.
All buses are green.
Conclusions:
I. All yellow are roses.
II. Some buses are yellow.
III. All yellow is green.
Option 1: Only conclusion III follows
Option 2: None of the conclusions follows
Option 3: Only conclusion II follows
Option 4: Only conclusion I follows
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Correct Answer: Only conclusion II follows
Solution : According to the statements, the following Venn diagram can be drawn –
Let's analyse the conclusions –
Conclusion I:
All yellow are roses – From the above Venn diagram, it is evident that the circles representing yellow and roses overlap each other and have some parts of their areas in common. So, from this, it can be concluded that some roses are yellow. Therefore, this conclusion does not follow.
Conclusion II:
Some buses are yellow – From the above Venn diagram, it is evident that the circles representing yellow and buses overlap each other and have some parts of their areas in common. So, from this, it can be concluded that some buses are yellow. Therefore, this conclusion follows.
Conclusion III:
All yellow is green – From the above Venn diagram, it is evident that the circles representing yellow and green overlap each other and have some parts of their areas in common. So, from this, it can be concluded that some yellow are green. Therefore, this conclusion does not follow.
So, only conclusion II follows according to the statements. Hence, the third option is correct.
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