# ch.7 :- Logic Based Venn Diagrams :- Exercise 4

✦ Directions for Q. No. 1 to 5 : Read the following information carefully and then answer the questions that follow:
In the following questions answers are based on the diagram given below, where the triangle represents doctors, the circle represents players and the rectangle represents the artists.

1. Which numbered space in the diagram represents doctors, who are also players and artists?
(a) 2     (b) 3     (c) 4    (d) 5     (e) None of these

Ans.(d)
The region 4 is common to triangle, circle and rectangle, and hence represents doctors who are players as well as artists.

2. Which numbered space in diagram represents artists,who are players?
(a) 6     (b) 7    (c) 8    (d) 4    (e) Non of these

Ans.(a)
The Region 4 is common to circle and rectangle only.

3. Which numbered space in the diagram represents artists,who are neither players nor doctors?
(a) 1    (b)  2    (c) 3    (d) 4    (e) Non of these

Ans.(a)
The Region 1 is not common to any other figure.

4. Which numbered space represents players, who are neither artists nor doctors?
(a) 1,2     (b) 3, 4     (c) 6, 7     (d) 7,8     (e) 1,5

Ans.(d)
The Regions 7 and 8 is not common to any other figure.

5. Which numbered space represents doctors, who are players but not artists?
(a) 2    (b) 3    (c) 4    (d) 5    (e) 1

Ans.(c)
The Region 4 is common to circle and triangle only.

✦Directions for Q. No. 6 to 8 : Read the following information and then answer the questions that follow In the Fig. the rectangle stands for philosopher, circle for historians and triangle for magicians

6. According to the above diagram, which one of the following statement is true?
(a) All philosophers are magicians but no magician is a historians
(b) All magicians are either historians Or philosophers
(c) Some philosophers are historians and some magicians are philosophers
(d) Some historians, who are philosophers, are magicians too
(e) None of the above

Ans.(c)
Because some portion of rectangle is common to them triangle and the circle.

7. According to the above diagram, which one of the following statement is true?
(a) All historians are magicians
(b) Some magicians are philosophers as well as historians
(c) All historians are either philosophers or magicians
(d) Some historians are philosophers
(e) None of the above

Ans.(d)
The circle and the rectangle have some areas in common

8. According to the above diagram, which one of the following statements is not true?
(a) Some magicians are philosophers
(b) No magician is historian
(c) Magicians, who are philosophers, are historians also
(d) Some philosophers are magicians
(e) None of the above

Ans.(c)
Because no portion of the figure shows the common space among the three figures.

✦Direction for Q. No. 9 to 12 : In the following figure, the smaller triangle represents the teachers, the big triangle represents the politicians, the circle represents the graduates, and the square represents the Members of Parliament. Different regions are being represented by letters of English alphabets.

9.Who among the following are graduates or teachers but not politicians?
(a) B, G     (b) G, H     (c) A, E    (d) E, F     (e) None of these.

Ans.(c)
Because A and E do not fall under the big triangular space

10. Who among the following politicians are graduates but not the members of parliament?
(a) B, C     (b) L, B     (c) D, L    (d) A, H, L     (e) B, G, C

Ans.(a)
Because Band C do not fall under the square

11. Who among the following politicians are neither teachers nor graduates?
(a) E, F     (b) D, E     (c) C, D    (d) L, H     (e) D, H

Ans.(d)
Because Land H do not fall under small triangular and circular space.

12. Who among the following members of parliament is a graduate as well as a teacher?
(a) G     (b) F     (c) C    (d) H     (e) E.

Ans.(b)
Because F is common to circle, square and the small triangle

✦Directions for Q. No. 13 to 17: Below is given a figure with four intersecting circles, each representing a group of persons having the quality written against it Study the figure carefully and answer the questions that follow:

13. People who are not laborious, enterprising and disciplined are represented by :
(a) Q     (b) T     (c) U     (d) V

Ans.(d)
People who are only studious are represented byV

14. The region which represents people who are not studious, but possess other three qualities, is denoted by:
(a) M     (b) N     (c) 0     (d)W

Ans.(c)
o shows the persons who are laborious, enterprising and disciplined

15. The region which represents the people who are enterprising, studious and disciplined but not laborious,is denoted by :
(a) Q      (b) P     (c) S     (d) T

Ans.(a)
Q represents the region of enterprising, studious and.disciplined people.

16. People who are not studious and disciplined but are laborious and enterprising both, are represented by:
(a) M     (b) N     (c) P     (d) K

Ans.(d)
Required region is represented by K

17. The people possessing all the qualities are represented by:
(a) 0     (b) N     (c) K     (d) Q

Ans.(b)
N shows the region common to all the four circles

✦Directions for Q. No. 18 to 23 : In the following figure, the circle stands for insurance agents, the square stands for hard working, the triangle stands for rural people and the rectangle stands for graduates. Study the figure carefully and answer the questions that follow:

18. Non rural and hard-working insurance agents who are graduates are indicated by the region:
(a) 5     (b) 7     (c) 9     (d) 10

Ans.(d)
Region 10 is common to circle, rectangle and square,hence represents the required region

19. Insurance agents who are neither graduates nor hard working but rural, are represented by the region
(a) 8     (b) 10     (c) 11     (d) 12

Ans.(d)

20. Hard-working, non-graduates, rural insurance agent are represented by the region:
(a) 6     (b) 7     (c) 9     (d) 12

Ans.(b)

21. Non-graduates insurance agents who are not hard working and who do not belong to rural areas are represented by the region:
(a) 5     (b) 6     (c) 8     (d) 1

Ans.(a)

22. Insurance agents who are graduates, hard-working and rural are represented by the region:
(a) 6     (b) 8     (c) 9     (d) 10