Deduction

(CAT 2001)

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 (e.g. if none of the women in the set B is a mother, then 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.

1. Given that X = M .D is such that X = D. Which of the following is true?

a. All dogs are mammals 

b. Some dogs are mammals

c. X = ϕ 

d. All mammals are dogs

2. If Y = F . (D . V) is not a null set, it implies that

a. all fish are vertebrates 

b. all dogs are vertebrates

c. some fish are dogs 

d. None of these

3. If Z = (P . D) ∪M, then

a. 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

4. If P . A = ϕ and P ∪ A = D, then which of the following is true?

a. Pluto and alsatians are dogs

b. Pluto is an alsatian

c. Pluto is not an alsatian

d. D is a null set

For answers click here.