Question : Directions: In the following question, some statements are given followed by some conclusions I and II. 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 follows from the given statements.
Statements:
Some cats are dogs.
All dogs are black.
Conclusions:
I. Some cats are black.
II. Some dogs are black.
Option 1: Neither conclusion I nor II follows
Option 2: Both conclusions I and II follow
Option 3: Only conclusion I follows
Option 4: Only conclusion II 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 black – From the Venn diagram, it is evident that the circles representing cats and black overlap each other and have a part of their area in common. So, from this, it can be concluded that some cats are black. Therefore, this conclusion follows.
Conclusion (II):
Some dogs are black – From the Venn diagram, it is evident that the circle representing dogs completely lies inside the circle representing black. So, from this, it can be concluded that all dogs are black. Thus, if all dogs are black then some dogs will definitely be black. So, this conclusion follows.
So, both conclusions follow. Hence, the second option is correct.
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