In the diagram given below, there is a circle, a square and a triangle dividing the region into five disjoint bounded areas. Each of these areas are labelled with number of players belonging to that area. The circle contains cricketers, the square contains football players and the triangle contains hockey players.Which one of the following is not correct?

There are some hockey players who play both cricket and football

Every hockey player plays football

Every cricket player plays either football or hockey

There are some hockey players who play both cricket and football

There are some football players who play neither cricket nor hockey

Directions: In these Questions, two statement P and Q are given. You may look into their logical acceptability and choose your answer.P: All A's are B's. all B's are C's. Therefore, all C's are A's.Q: Some A's are B's. All B's are C's. Therefore, some A's are C's.

Both P & Q are wrong or doubtful

P is correct and Q is wrong or Doubtful

P is wrong or doubtful and Q is correct

Both P & Q are wrong or doubtful

453 + Mcqs in Venn Diagram in Discrete Mathematics Page 7 McqOptions

301.	Ram, Mahesh and Mohan play badminton. Mahesh, Ramesh and Pramod play tennis and Mahesh, Ramesh and Ram play chess. Who plays chess and badminton, but not tennis ?
A.	Mahesh
B.	Pramod
C.	Ramesh
D.	Ram
Answer» E.

Discussion

302.	How many passed in both Mathematics and at least one more subject?
A.	48
B.	210
C.	103
D.	203
Answer» E.

Discussion

303.	Out of a total of 120 musicians in a club, 5% can play all the three instruments, guitar, violin and flute. It so happens that the number of musicians who can play any two and only two of the above instruments is 30. The number of musicians who can play the guitar alone is 40. What is the total number of those who can play violin alone or flute alone ?
A.	45
B.	44
C.	38
D.	30
Answer» C. 38

Discussion

304.	How many students like only one of the given subjects?
A.	48
B.	45
C.	81
D.	72
Answer» E.

Discussion

305.	In the given figure, how many cups are blue but not bottles?
A.	97
B.	109
C.	28
D.	68
Answer» B. 109

Discussion

306.	In the Following figure, square represents Artists, triangle represents Military officers, circle represents Collectors and rectangle represents Fathers. Which set of letters represents collectors who are either military officers or fathers?
A.	F, C
B.	D, E
C.	A, B, G
D.	H, E, D
Answer» D. H, E, D

Discussion

307.	How many students do not play any one of the games?
A.	5
B.	2
C.	7
D.	1
Answer» D. 1

Discussion

308.	In the following figure, the smaller triangle represents the teacher, the big triangle represents the politician, the circle represents the graduates and the square represents the members of parliament. Each different region is being represented by letters of the English alphabet.Who among the following members of parliament is a graduate as well as a teacher?
A.	G
B.	F
C.	B
D.	H
Answer» C. B

Discussion

309.	By which number, the trained unmarried lecturers in the college are represented?A. 6B. 5C. 7D. 4
A.	C
B.	B
C.	D
D.	A
Answer» D. A

Discussion

310.	In the following figure, rectangle represents Physicians, circle represents racers, triangle represents Writers and square represents Mothers. Which set of letters represents Mothers who are not Racers?
A.	FGH
B.	ECA
C.	DFG
D.	DGFI
Answer» D. DGFI

Discussion

311.	Among 45 students of a class, 26 attend Yoga class, 28 attend Gymnastic class and 5 students attend neither Yoga nor Gymnastic class. How many students attend both Yoga and Gymnastic classes?
A.	16
B.	14
C.	12
D.	10
Answer» C. 12

Discussion

312.	In the given figure, how many triangles are large but not equilateral?
A.	17
B.	19
C.	18
D.	15
Answer» C. 18

Discussion

313.	In the following figure, rectangle represents Plumbers, circle represents Essayists, tringle represents Divers and square represents Asians. Which set of letters represents Asians who are Essayists?
A.	EDB
B.	IED
C.	ED
D.	FED
Answer» D. FED

Discussion

314.	15 families of Ananda Colony wanted to go for small evening picnic and decided to bring their own food packs. 7 families brought French fries and 8 families brought Bread and Toast. But three families brought none of these two but Biryani. How many of them brought both French fries and Bread and Toast?
A.	5
B.	6
C.	4
D.	3
Answer» E.

Discussion

315.	In a class of 180 students, 90 students speak Bengali, 70 students speak Marathi and 50 students do NOT speak any of these two languages. How many students speak both languages?
A.	30
B.	40
C.	60
D.	50
Answer» B. 40

Discussion

316.	In the diagram given below, there is a circle, a square and a triangle dividing the region into five disjoint bounded areas. Each of these areas are labelled with number of players belonging to that area. The circle contains cricketers, the square contains football players and the triangle contains hockey players.Which one of the following is not correct?
A.	Every hockey player plays football
B.	Every cricket player plays either football or hockey
C.	There are some hockey players who play both cricket and football
D.	There are some football players who play neither cricket nor hockey
Answer» C. There are some hockey players who play both cricket and football

Discussion

317.	60 students participated in one or more of the three competitions, i. e. Quiz, Extempore and Debate. A total of 22 students participated either in Quiz only or in Extempore only. 4 students participated in all three competitions. A total of 14 students participated in any of the two competitions only. How many students participated in Debated only?
A.	22
B.	20
C.	11
D.	14
Answer» C. 11

Discussion

318.	In the given figure, how many leather bags are not red?
A.	29
B.	76
C.	43
D.	51
Answer» E.

Discussion

319.	Choose the Venn diagram that shows the best of the three classes below:(1) (2) (3) (4) State, District, City
A.	d
B.	c
C.	b
D.	a
Answer» E.

Discussion

320.	In the following figure, square represents Translators, triangle represents Exporters, circle represents Professors and rectangle represents Fathers. Which set of letters represents Translators and Exporters who are also Professors?
A.	F, G, H
B.	E, C, D
C.	A, C
D.	B, F
Answer» D. B, F

Discussion

321.	In the following figure, the triangle represents girls, the circle athletes, the rectangle boys and the square disciplined.The boys who are athletes and disciplined are indicated by which number?
A.	1
B.	2
C.	6
D.	10
Answer» C. 6

Discussion

322.	In the given figure, how many metallic balls are also heavy?
A.	97
B.	71
C.	31
D.	66
Answer» D. 66

Discussion

323.	In the following figure, rectangle represents Authors, circle represents Food stylists, triangle represents Potters and square represents Cricketers. Which set of letters represents Authors who are either Food stylists or Potters?
A.	ACH
B.	AC
C.	CH
D.	C
Answer» B. AC

Discussion

324.	In the following diagram, the triangle represents ‘dancers’, the circle represents ‘swimmers’, the rectangle represents 3 ‘students’ and the square represents ‘cricket fans’. The numbers in different segments show the number of persons.How many student dancers are swimmers but not cricket fans?
A.	15
B.	10
C.	3
D.	13
E.	7
Answer» C. 3

Discussion

325.	In the given diagram the rectangle represents males, the circle represents actors and the triangle singers. How many represents male singers?
A.	3
B.	5
C.	8
D.	6
Answer» D. 6

Discussion

326.	How many like only science?
A.	29
B.	15
C.	26
D.	19
Answer» D. 19

Discussion

327.	Look at the given Venn Diagram carefully and select from the given option the one which represent the group of people who are not businessmen but are healthy and married.
A.	C + D
B.	I + J
C.	G + H + K
D.	E + F
Answer» B. I + J

Discussion

328.	In NGO Colony, the people are classified into four different groups as given in the following figure: the rectangle represents men, the triangle represents educated, the circle represents urban and the square represents government employees.Which one of the following represents the educated men who are NOT urban?
A.	9
B.	4
C.	11
D.	5
Answer» D. 5

Discussion

329.	In the following figure, rectangle represents Opticians, circle represents Curators, triangle represent Campers and square represents Europeans. Which set of letters Opticians who are either Europeans or Campers?
A.	IDH
B.	DEF
C.	CID
D.	IBD
Answer» B. DEF

Discussion

330.	In the following figure, rectangle represent Reporters, circle represents Artists, triangle represents Mountain climbers and square represents Football players. Which set of letters represents Reporters who are Mountain climbers?
A.	AH
B.	BG
C.	CF
D.	LM
Answer» B. BG

Discussion

331.	Directions: In these Questions, two statement P and Q are given. You may look into their logical acceptability and choose your answer.P: All A's are B's. all B's are C's. Therefore, all C's are A's.Q: Some A's are B's. All B's are C's. Therefore, some A's are C's.
A.	Both P & Q are true
B.	P is correct and Q is wrong or Doubtful
C.	P is wrong or doubtful and Q is correct
D.	Both P & Q are wrong or doubtful
Answer» D. Both P & Q are wrong or doubtful

Discussion

332.	In the following figure, square represents pharmacists, triangle represents Dancers, circle represents Gynecologists and rectangle represents Women. Which set of letters represents Gynecologists who are neither Women nor Dancers?
A.	F,B,H
B.	B,D,H
C.	D,E,A
D.	C,H
Answer» E.

Discussion

333.	How many Leopard are either lion or tiger or both?
A.	35
B.	55
C.	90
D.	95
Answer» D. 95

Discussion

334.	In the following figure, rectangle represents Physicians, circle represents floral designers, triangle represents Sculptors and square represents Americans. Which set of letters represents Americans who are either Floral designers or Sculptors?
A.	FGDH
B.	FGK
C.	FHJD
D.	GK
Answer» B. FGK

Discussion

335.	In the following figure, square represents Therapists, triangle represents Geneticists, circle represents yoga and rectangle represents Fathers. Which set of letters represents yoga practitioners who are neither geneticists nor fathers?
A.	C, B
B.	E, A
C.	G, C
D.	F, G
Answer» E.

Discussion

336.	According to the given Venn diagram, the total number of students in the class is ______ .
A.	53
B.	55
C.	54
D.	56
Answer» C. 54

Discussion

337.	Directions: Study the following figure and answer the question that follows:Which letters represent the artists who are doctors as well as dancers but not scientists?
A.	L and H
B.	G and C
C.	G and H
D.	C and H
Answer» C. G and H

Discussion

338.	In the given figure, how many people speak only Italian and only French Language?
A.	21
B.	16
C.	27
D.	20
Answer» B. 16

Discussion

339.	In the given figure, circles represent students studying three different subjects. How many students study all the three subjects?
A.	4
B.	2
C.	3
D.	1
Answer» D. 1

Discussion

340.	In the following figure, square represents Chinese, triangle represents dancers, circle represents male and rectangle represents architects. Which set of letters represents dancers who are male?
A.	DEIG
B.	DEF
C.	IGH
D.	GEF
Answer» E.

Discussion

341.	In the following figure, square represents lawyers, triangle represents cyclists, circle represents men and rectangle represents post-graduates. Which set of letters represents men who are not cyclists?
A.	FGBK
B.	CDIJ
C.	JCKB
D.	JIHG
Answer» C. JCKB

Discussion

342.	How many families have at least one vehicle?
A.	185
B.	135
C.	165
D.	Cannot be determined
Answer» B. 135

Discussion

343.	In the given figure, how many pens are of iron but are not hard?
A.	19
B.	15
C.	49
D.	31
Answer» B. 15

Discussion

344.	In the following diagram, the triangle represents ‘cricket players’, the circle represents ‘swimmers’ and the rectangle represents ‘students’. The numbers in different segments show the number of persons.How many students are swimmers but not cricket players?
A.	17
B.	13
C.	8
D.	18
E.	11
Answer» B. 13

Discussion

345.	In the given figure, A represents people liking APPLES, B represents people liking BANANAS, C represents people liking CHIKOO. How many people like ONLY APPLES?
A.	4
B.	10
C.	6
D.	3
Answer» C. 6

Discussion

346.	How many students play exactly two games?
A.	7
B.	13
C.	5
D.	16
Answer» E.

Discussion

347.	In the following figure, rectangle represents Web designers, circle represents Equestrians, triangle represents Poets and square represents Joggers. Which set of letter represents Joggers who are both Equestrians as well as Poets?
A.	BDG
B.	ABDG
C.	BD
D.	D
Answer» E.

Discussion

348.	How many kids do not like volleyball?
A.	15
B.	25
C.	35
D.	45
Answer» D. 45

Discussion

349.	Out of 60 customers, 10 chose service 1 and 2, 15 chose service 2 and 3 and 5 chose service 1 and 3, 15 chose only service 2. 20 chose service 1, 35 chose service 2, and 30 chose service 3. How many chose all the three services?
A.	2
B.	5
C.	4
D.	3
Answer» C. 4

Discussion

350.	In the following figure, rectangle represents Authors, circle represents Choreographers, triangle represents Playwrights and square represents Asians. Which set of letters represents Authors who are not Asians?
A.	HG
B.	FE
C.	DA
D.	IC
Answer» E.

Discussion

Explore topic-wise MCQs in Discrete Mathematics.

Ram, Mahesh and Mohan play badminton. Mahesh, Ramesh and Pramod play tennis and Mahesh, Ramesh and Ram play chess. Who plays chess and badminton, but not tennis ?

How many passed in both Mathematics and at least one more subject?

How many students like only one of the given subjects?

In the given figure, how many cups are blue but not bottles?

In the Following figure, square represents Artists, triangle represents Military officers, circle represents Collectors and rectangle represents Fathers. Which set of letters represents collectors who are either military officers or fathers?

How many students do not play any one of the games?

By which number, the trained unmarried lecturers in the college are represented?A. 6B. 5C. 7D. 4

In the following figure, rectangle represents Physicians, circle represents racers, triangle represents Writers and square represents Mothers. Which set of letters represents Mothers who are not Racers?

Among 45 students of a class, 26 attend Yoga class, 28 attend Gymnastic class and 5 students attend neither Yoga nor Gymnastic class. How many students attend both Yoga and Gymnastic classes?

In the given figure, how many triangles are large but not equilateral?

In the following figure, rectangle represents Plumbers, circle represents Essayists, tringle represents Divers and square represents Asians. Which set of letters represents Asians who are Essayists?

In a class of 180 students, 90 students speak Bengali, 70 students speak Marathi and 50 students do NOT speak any of these two languages. How many students speak both languages?

In the given figure, how many leather bags are not red?

Choose the Venn diagram that shows the best of the three classes below:(1) (2) (3) (4) State, District, City

In the following figure, square represents Translators, triangle represents Exporters, circle represents Professors and rectangle represents Fathers. Which set of letters represents Translators and Exporters who are also Professors?

In the following figure, the triangle represents girls, the circle athletes, the rectangle boys and the square disciplined.The boys who are athletes and disciplined are indicated by which number?

In the given figure, how many metallic balls are also heavy?

In the following figure, rectangle represents Authors, circle represents Food stylists, triangle represents Potters and square represents Cricketers. Which set of letters represents Authors who are either Food stylists or Potters?

​In the given diagram the rectangle represents males, the circle represents actors and the triangle singers. How many represents male singers?

How many like only science?

Look at the given Venn Diagram carefully and select from the given option the one which represent the group of people who are not businessmen but are healthy and married.

In the following figure, rectangle represents Opticians, circle represents Curators, triangle represent Campers and square represents Europeans. Which set of letters Opticians who are either Europeans or Campers?

In the following figure, rectangle represent Reporters, circle represents Artists, triangle represents Mountain climbers and square represents Football players. Which set of letters represents Reporters who are Mountain climbers?

Directions: In these Questions, two statement P and Q are given. You may look into their logical acceptability and choose your answer.P: All A's are B's. all B's are C's. Therefore, all C's are A's.Q: Some A's are B's. All B's are C's. Therefore, some A's are C's.

In the following figure, square represents pharmacists, triangle represents Dancers, circle represents Gynecologists and rectangle represents Women. Which set of letters represents Gynecologists who are neither Women nor Dancers?

How many Leopard are either lion or tiger or both?

In the following figure, rectangle represents Physicians, circle represents floral designers, triangle represents Sculptors and square represents Americans. Which set of letters represents Americans who are either Floral designers or Sculptors?

In the following figure, square represents Therapists, triangle represents Geneticists, circle represents yoga and rectangle represents Fathers. Which set of letters represents yoga practitioners who are neither geneticists nor fathers?

According to the given Venn diagram, the total number of students in the class is ______ .

Directions: Study the following figure and answer the question that follows:Which letters represent the artists who are doctors as well as dancers but not scientists?

In the given figure, how many people speak only Italian and only French Language?

In the given figure, circles represent students studying three different subjects. How many students study all the three subjects?

In the following figure, square represents Chinese, triangle represents dancers, circle represents male and rectangle represents architects. Which set of letters represents dancers who are male?

In the following figure, square represents lawyers, triangle represents cyclists, circle represents men and rectangle represents post-graduates. Which set of letters represents men who are not cyclists?

How many families have at least one vehicle?

In the given figure, how many pens are of iron but are not hard?

In the following diagram, the triangle represents ‘cricket players’, the circle represents ‘swimmers’ and the rectangle represents ‘students’. The numbers in different segments show the number of persons.How many students are swimmers but not cricket players?

In the given figure, A represents people liking APPLES, B represents people liking BANANAS, C represents people liking CHIKOO. How many people like ONLY APPLES?

How many students play exactly two games?

In the following figure, rectangle represents Web designers, circle represents Equestrians, triangle represents Poets and square represents Joggers. Which set of letter represents Joggers who are both Equestrians as well as Poets?

How many kids do not like volleyball?

Out of 60 customers, 10 chose service 1 and 2, 15 chose service 2 and 3 and 5 chose service 1 and 3, 15 chose only service 2. 20 chose service 1, 35 chose service 2, and 30 chose service 3. How many chose all the three services?

In the following figure, rectangle represents Authors, circle represents Choreographers, triangle represents Playwrights and square represents Asians. Which set of letters represents Authors who are not Asians?

In the given diagram the rectangle represents males, the circle represents actors and the triangle singers. How many represents male singers?