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 plums are pomegranates.
Some plums are lemons.
Conclusions:
I. Some pomegranates are lemons.
II. No lemon is a pomegranate.
III. Some pomegranates are plums.
Option 1: Only conclusion III follows
Option 2: Only conclusion I follows
Option 3: Only conclusions I and III follow
Option 4: Only conclusions I and II follow
Correct Answer: Only conclusions I and III follow
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyze the conclusions –
Conclusion (I):
Some pomegranates are lemons – From the Venn diagram, it is evident that the circles representing pomegranates and lemons overlap and have some parts of their area in common. Thus, it can be concluded that some pomegranates are lemons.
Conclusion (II):
No lemon is a pomegranate – From the Venn diagram, it is evident that the circles representing pomegranates and lemons overlap and have some parts of their area in common. Thus, this conclusion does not follow.
Conclusion (III):
Some pomegranates are plums – From the Venn diagram, it is evident that some parts of the circle representing pomegranates lie inside the circle representing plums while some lie outside. Thus, it can be concluded that some pomegranates are plums.
So, only conclusions I and III follow. Hence, the third option is correct.
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