Question : Directions: 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 follow(s) from the statements.
Statements:
No cup is a plate.
All cups are utensils.
Some bottles are cups.
Conclusions:
I. Some utensils are not plates.
II. Some bottles are not plates.
III. No bottle is a plate.
Option 1: Only conclusions I and II follow
Option 2: Only conclusions II and III follow
Option 3: All conclusions follow
Option 4: Only conclusions I and III follow
Correct Answer: Only conclusions I and II follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some utensils are not plates – From the Venn diagram, it is evident that no cups are plates. So, some parts of the circle representing utensils that lie inside the circle representing cups will not be plates. Therefore, it can be concluded that some utensils are not plates.
Conclusion (II):
Some bottles are not plates – From the Venn diagram, it is evident that no cups are plates. So, some parts of the circle representing bottles that lie inside the circle representing cups will not be plates. Therefore, it can be concluded that some bottles are not plates.
Conclusion (III):
No bottle is a plate – From the Venn diagram, it is evident that no cups are plates. So, some parts of the circle representing bottles that lie inside the circle representing cups will not be plates. Therefore, it can be concluded that some bottles are not plates. So, this conclusion does not follow.
So, only conclusions I and II follow. Hence, the first option is correct.
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