### CAT 2001 Question Paper Question 98

Instructions

Directions for the following four questions: Answer the questions based on the following information.

A and B are two sets (e.g. A = Mothers, B = Women).

The elements that could belong to both the sets (e.g. women who are mothers) is given by the set $$C = A \cap B$$.

The elements which could belong to either A or B, or both, is indicated by the set $$D = A \cup B$$ .

A set that does not contain any elements is known as a null set represented by $$\phi$$(e.g. if none of the women in the set B is a mother, then $$C = A \cap B$$ is a null set, or C = $$\phi$$).

Let ‘V’ signify the set of all vertebrates, ‘M’ the set of all mammals, ‘D’ dogs, ‘F’ fish, ‘A’ alsatian and ‘P’, a dog named Pluto.

Question 98

# If $$Y = F \cap (D \cap V)$$ is not a null set, it implies that

Solution

We know that all dogs are vertebrates. Hence $$D \cap V)$$ = D . Ahead it is given that $$Y = F \cap D$$ is not a null set  which implies that some fish are dogs. Hence , option C.