TheCATExam
Sign in

CAT 2001 — DILR Question 42

2 SetsEasy
Passage / Data

Answer the following question based on the information given below.

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.B. The elements which could belong to either A or B, or both, is indicated by the set D = A ∪ B. A set that does not contain any elements is known as a null set, represented by ϕ (for example, if none of the women in the set B is a mother, they C = A.B is a null set, or C = ϕ).

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.

If Z = (P.D) ∪ M, then

Answer & solution

  • The elements of Z consist of Pluto the dog or any other mammal.

  • B

    Z implies any dog or mammal.

  • C

    Z implies Pluto or any dog that is a mammal.

  • D

    Z is a null set.

Solution

Z = (P.D) ∪ M

P.D means a dog called Pluto and P ∪ M means Pluto the dog and the other mammals.

Hence, option (a).

CAT 2001 DILR Q42: If Z = (P.D) ∪ M, then — Solution | TheCATExam