Question : Directions: Two statements are given followed by two conclusions numbered I and II. 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:
All dogs are cats.
No cat is a rat.
Conclusions:
I. Some rats are cats.
II. Some dogs are rats.
Option 1: Neither conclusion I nor II follows
Option 2: Only conclusion I follows
Option 3: Both conclusions I and II follow
Option 4: Only conclusion II follows
Correct Answer: Neither conclusion I nor II follows
Solution :
The possible Venn diagram for the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some rats are cats – From the above diagram, it is clear that there is a negative relation between rats and cats. So, this conclusion doesn't follow.
Conclusion (II):
Some dogs are rats – From the above diagram, it is clear that no cats are rats, and the circle of dogs is completely inside the circle of cats. So, this conclusion doesn't follow.
So, neither conclusion I nor conclusion II follows. Hence, the first option is correct.
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