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:
Some cats are dogs.
Some dogs are rats.
All rats are tigers.
Conclusions:
I. Some tigers are cats.
II. Some tigers are dogs.
III. Some rats are dogs.
Option 1: Only conclusions II and III follow
Option 2: Only conclusions I follows
Option 3: Only conclusions I and II follow
Option 4: Only conclusions I and III follow
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Correct Answer: Only conclusions II and III follow
Solution :
The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some tigers are cats – From the Venn diagram, there is no definite relation between tigers and cats. Therefore, this conclusion is false.
Conclusion (II):
Some tigers are dogs – From the Venn diagram, the circle of the dog intersects with the circle of the tiger and has a common area between them. Therefore, this conclusion is true.
Conclusion (III):
Some rats are dogs – From the Venn diagram, the circle of the dog intersects the circle of the rat and has a common area between them. Therefore, this conclusion is true.
So, only conclusions II and III follow. Hence, the first option is correct.
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