Question : Directions: In the following question, two statements are given followed by four conclusions I, II, III and IV. You have to consider the two 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 cats are dogs.
No dog is a toy.
Conclusions:
I. Some dogs are cats.
II. Some Toys are cats.
III. Some cats are not toys.
IV. All toys are cats.
Option 1: Only Conclusions I and III follow
Option 2: Only Conclusions II and III follow
Option 3: Only Conclusions I and II follow
Option 4: Only Conclusion I follows
Correct Answer: Only Conclusions I and III follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some dogs are cats – From the Venn diagram, it is evident that the circles representing dogs and cats overlap and have a part of their area in common. So, from this, it can be concluded that some dogs are cats. Therefore, this conclusion follows.
Conclusion (II):
Some Toys are Cats – From the Venn diagram, it is evident that there is no direct relation between toys and cats. So, no definite relation can be drawn. Therefore, this conclusion does not follow.
Conclusion (III):
Some cats are not toys – From the Venn diagram, some cats are dogs and no dog is a toy, therefore, part of the cat which is a dog is definitely not a toy. Therefore, this conclusion follows.
Conclusion (IV):
All toys are cats – From the Venn diagram, it is evident that there is no direct relation between toys and cats. So, no definite relation can be drawn. Therefore, this conclusion does not follow.
Therefore, only Conclusion I and Conclusion III are correct. Hence, the first option is correct.
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