Given below is a diagram of three circles A, B and C over-lapping each other.…
2014
Given below is a diagram of three circles A, B and C over-lapping each other. The circle A represents the class of honest people, the circle B represents the class of sincere people and circle C represents the class of politicians. p, q, r, s, U, X, Y represent different regions. Select the code that represents the region indicating the class of honest politicians who are not sincere. Codes :
Answer: D. s — Concept — In a Venn diagram every circle stands for a class, and a region belongs to exactly those classes whose circles enclose it. A description of the form…
- A.
X
- B.
q
- C.
p
- D.
s
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Correct answer: D
Concept — In a Venn diagram every circle stands for a class, and a region belongs to exactly those classes whose circles enclose it. A description of the form 'in two given classes but not in a third' therefore picks the region that lies inside both of those two circles and outside the third circle; in set language it is the intersection of the first two classes, minus the third.
Application — Here circle A is the class of honest people, circle B the class of sincere people and circle C the class of politicians. The class asked for, honest politicians who are not sincere, is made of members of A and of C that lie outside B, that is the region (A and C) minus B.
Honest: the region must lie inside circle A.
Politicians: the region must also lie inside circle C.
Not sincere: the region must lie outside circle B.
The only region of this diagram that lies inside A and inside C while lying outside B is the one labelled s.
Cross-check — reading every region of the diagram against the three classes:
Region | Lies inside | Class it denotes |
|---|---|---|
U | A only | Honest people who are neither sincere nor politicians |
X | B only | Sincere people who are neither honest nor politicians |
Y | C only | Politicians who are neither honest nor sincere |
r | A and B, outside C | Honest and sincere people who are not politicians |
s | A and C, outside B | Honest politicians who are not sincere |
q | B and C, outside A | Sincere politicians who are not honest |
p | A, B and C | People who are honest, sincere and politicians at the same time |
Only one region satisfies all three conditions at once, so the required region is s.