Question : Directions: 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 shops are rooms.
All rooms are kitchens.
Conclusions:
I. All shops are kitchens.
II. Some shops are kitchens.
III. Some rooms are shops.
IV. All kitchens are shops.
Option 1: Only I and IV follow
Option 2: Only II follows
Option 3: Only II and III follow
Option 4: Only I follows
Correct Answer: Only II and III follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
All shops are kitchens – From the Venn diagram, it is evident that the circles representing shops and kitchens overlap and have a part of their areas in common. So, from this, it can be concluded that some shops are kitchens. Therefore, this conclusion does not follow.
Conclusion (II):
Some shops are kitchens – From the Venn diagram, it is evident that the circles representing shops and kitchens overlap and have a part of their areas in common. So, from this, it can be concluded that some shops are kitchens. Therefore, this conclusion follows.
Conclusion (III):
Some rooms are shops –
From the Venn diagram, it is evident that the circles representing shops and rooms overlap and have a part of their areas in common. So, from this, it can be concluded that some rooms are shops. Therefore, this conclusion follows.
Conclusion (IV):
All kitchens are shops –
From the Venn diagram, it is evident that the circles representing shops and kitchens overlap and have a part of their areas in common. So, from this, it can be concluded that some kitchens are shops. Therefore, this conclusion does not follow.
So, only conclusions II and III follow. Hence, the third option is correct.
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