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Q #41
:

Directions: 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 = AOB. A set that does not contain any elements is known as a null set, represented by @(for example, if none of the women in the set B is a mother, then C = A.B. is a null set, or C = @. 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 P.A. = @ and POA = D, then which of the following is true?

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Explanation: P.A = @ implies P into is not an Alsatian, but POA = D implies both P and A are dogs.

Q #42
:

Directions: 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 = AOB. A set that does not contain any elements is known as a null set, represented by @(for example, if none of the women in the set B is a mother, then C = A.B. is a null set, or C = @. 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 y = FO (D.V.) is not a null set, it implies that:

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Explanation: Fish   (Dogs ∩    Vertebrate) ≠  @ implies that some elements are common between Fish and Dogs.


Q #43
:

Directions: 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 = AOB. A set that does not contain any elements is known as a null set, represented by @(for example, if none of the women in the set B is a mother, then C = A.B. is a null set, or C = @. 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.) OM, then

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Explanation: Z = (Pluto ∩  Dogs)   Mammals = Pluto   Mammals.



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