Question : Directions: Below some statements are given, followed by some conclusions. 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, if any follow from the given statements.
Statements:
Some spoons are cups.
Some cups are bottles.
All bottles are mugs.
Conclusions:
I. Some mugs are cups.
II. Some cups are bottles.
III. Some spoons are mugs.
Option 1: Either I or II and III follow
Option 2: Only II follows
Option 3: Only I and II follow
Option 4: All follow
Correct Answer: Only 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 mugs are cups –
From the Venn diagram, it is evident that the circles representing mugs and cups overlap and have a part of their area in common. So, from this, it can be concluded that some mugs are cups. Therefore, this conclusion follows.
Conclusion (II):
Some cups are bottles –
From the Venn diagram, it is evident that the circles representing cups and bottles overlap and have a part of their area in common. So, from this, it can be concluded that some cups are bottles. Therefore, this conclusion follows.
Conclusion (III):
Some spoons are mugs –
From the Venn diagram, it is evident that there is no direct relation between spoons and mugs. So, no definite relation can be drawn. Therefore, this conclusion doesn't follow.
So, only the conclusion I and II follow. Hence, the third option is correct.
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