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CAT 2001 — DILR Question 40

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.

Given that X = M.D is such that X = D, which of the following is true?

Answer & solution

Correct answer: All dogs are mammals.

  • All dogs are mammals.

  • B

    Some dogs are mammals.

  • C

    X = ϕ

  • D

    All mammals are dogs.

Solution

X = M.D implies some dogs are mammals and X = D implies the set of dogs.

This implies all dogs are mammals.

Hence, option (a).

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CAT 2001 DILR Q40: Given that X = M.D is such that X = D, which of the following is true? — Solution | TheCATExam