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:
Some cats are rats.
All rats are mice.
Conclusions:
I. Some cats are mice.
II. Some mice are cats.
Option 1: Both conclusions I and II follow
Option 2: Only conclusion II follows
Option 3: Neither conclusion I nor II follows
Option 4: Only conclusion I follows
Correct Answer: Both conclusions 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 cats are mice – From the given Venn diagram, the circle of mice intersects the circle of cats and has a common area between them. Therefore, this conclusion is true.
Conclusion (II):
Some mice are cats – From the given Venn diagram, the circle of mice intersects the circle of cats and has a common area between them. Therefore, this conclusion is true.
So, both conclusions I and II follow. Hence, the first option is correct.
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