Given below is a diagram of three circles A, B & C inter-related with each…

2014

Given below is a diagram of three circles A, B & C inter-related with each other. The circle A represents the class of Indians, the circle B represents the class of scientists and circle C represents the class of politicians. p, q, r, s ... represent different regions. Select the code containing the region that indicates the class of Indian scientists who are not politicians.

Three overlapping circles: A represents Indians, B represents scientists, and C represents politicians. Region p is the overlap of A and C outside B; q is the overlap of A, B and C; r is the overlap of B and C outside A; and s is the overlap of A and B outside C.

Codes :

Answer: B. s onlyConcept: In a class diagram, each circle stands for one class, and every labelled region stands for exactly one membership signature — the region belongs to…

  1. A.

    q and s only

  2. B.

    s only

  3. C.

    s and r only

  4. D.

    p, q and s only

Attempted by 4 students.

Show answer & explanation

Correct answer: B

Concept: In a class diagram, each circle stands for one class, and every labelled region stands for exactly one membership signature — the region belongs to every circle that encloses it and to no circle that leaves it out. A description of the form "X that are Y but are not Z" therefore picks out the single region that lies inside the X-circle and the Y-circle while lying outside the Z-circle.

Application: Here circle A is the class of Indians, circle B is the class of scientists and circle C is the class of politicians. The phrase "Indian scientists who are not politicians" imposes three conditions at once — inside A, inside B, and outside C. In the given drawing, the lens shared by circles A and B has two parts: the upper part that also lies inside C, and the lower part that lies outside C. The lower part is labelled s, so s is exactly the set of people who are Indian and scientists and not politicians. Hence the required code is s.

Cross-check: Each of the other labelled regions fails at least one of the three conditions:

  • q lies inside all three circles, so every member of q is a politician; including q would violate the "not politicians" condition.

  • p lies inside A and C but outside B — Indians who are politicians and are not scientists.

  • r lies inside B and C but outside A — scientists who are politicians and are not Indians.

Every other code adds at least one of p, q or r to s, and each of those regions either brings in politicians or brings in people outside circle A. The region s alone meets inside-A, inside-B and outside-C together, so the required code is s.

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