Set Theory Quiz 1

Question 1

Time: 00:00:00
In a class of 345 students, the students who took English, Math, and Science are equal in number. There are 30 students who took both English and math, 26 who took both math and science, 28 who took science and English and 14 who took all the 3 subjects. Answer the following question according to the data given above. How many students have taken only one subject?

286

286

124

124

246

246

108

108

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Question 2

Time: 00:00:00
Set A = {2, 3, 5, 6, 7}, Set B = {a, b, c}. How many onto functions can be defined from Set B to Set A?

2

2

3

3

4

4

None of the above

None of the above

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Question 3

Time: 00:00:00
Set P comprises all multiples of 4 less than 500. Set Q comprises all odd multiples of 7 less than 500, Set R comprises all multiples of 6 less than 500. How many elements are present in P∪Q∪R?

202

202

243

243

228

228

186

186

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Question 4

Time: 00:00:00
How many of the following statements have to be true?

i. No year can have 5 Sundays in the month of May and 5 Thursdays in the month of June.

ii. If Feb 14th of a certain year is a Friday, May 14th of the same year cannot be a Thursday

iii. If a year has 53 Sundays, it can have 5 Mondays in the month of May.

1

1

2

2

3

3

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Statement (I): No year can have 5 Sundays in the month of May and 5 Thursdays in the month of June. A year has 5 Sundays in the month of May => it can have 5 each of Sundays, Mondays and Tuesdays, or 5 each of Saturdays, Sundays and Mondays, or 5 each of Fridays, Saturdays and Sundays. Or, the last day of the Month can be Sunday, Monday or Tuesday. Or, the 1st of June could be Monday, Tuesday or Wednesday. If the first of June were a Wednesday, June would have 5 Wednesdays and 5 Thursdays. So, statement I need not be true. Statement (II): If Feb 14th of a certain year is a Friday, May 14th of the same year cannot be a Thursday From Feb 14 to Mar 14, there are 28 or 29 days, 0 or 1 odd day Mar 14 to Apr 14, there are 31 days, or 3 odd days Apr 14 to May 14 there are 30 days or 2 odd days So, Feb 14 to May 14, there are either 5 or 6 odd days So, if Feb 14 is Friday, May 14 can be either Thursday or Wednesday. So, statement II need not be true. Statement (III): If a year has 53 Sundays, it can have 5 Mondays in the month of May Year has 53 Sundays => It is either a non-leap year that starts on Sunday, or leap year that starts on Sunday or Saturday. Non-leap year starting on Sunday: Jan 1st = Sunday, Jan 29th = Sunday. Feb 5th is Sunday. Mar 5th is Sunday, Mar 26th is Sunday. Apr 2nd is Sunday. Apr 30th is Sunday, May 1st is Monday. May will have 5 Mondays. So, statement III can be true.

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Question 5

Time: 00:00:00
John was born on Feb 29th of 2012 which happened to be a Wednesday. If he lives to be 101 years old, how many birthdays would he celebrate on a Wednesday?

3

3

4

4

5

5

1

1

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Question 6

Time: 00:00:00
Of 60 students in a class, anyone who has chosen to study maths elects to do physics as well. But no one does maths and chemistry, 16 do physics and chemistry. All the students do at least one of the three subjects and the number of people who do exactly one of the three is more than the number who do more than one of the three. What are the maximum and a minimum number of people who could have done Chemistry only?

40, 0

40, 0

28, 0

28, 0

38, 2

38, 2

44, 0

44, 0

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Question 7

Time: 00:00:00
In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, those whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects?

19

19

41

41

21

21

57

57

26

26

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Question 8

Time: 00:00:00
Among a group of people, 40% liked red, 30% liked blue and 30% liked green. 7% liked both red and green, 5% liked both red and blue, 10% liked both green and blue. If 86% of them liked at least one color, what percentage of people liked all three?

6

6

8

8

None

None

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Question 9

Time: 00:00:00
In a group, there were 115 people whose proofs of identity were being verified. Some had passport, some had voter id and some had both. If 65 had passport and 30 had both, how many had voter id only and not passport?

30

30

50

50

80

80

None of the above

None of the above

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Question 10

Time: 00:00:00
If ∪ = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U. B = {2, 4} A = {0} C = {1, 9, 5, 13} D = {5, 11, 1} E = {13, 7, 9, 11, 5, 3, 1} F = {2, 3, 4, 5}

CDE

CDE

DEF

DEF

BAD

BAD

ADF

ADF

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["0","40","60","80","100"]
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February 4, 2021