Grade 10 Mathematics · Interactive Student Edition
Exercise 1.1: Two Sets
Student-friendly practice with searchable questions, step-by-step reveals, and mobile-ready layout.
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Word Problems
Question
Complete Question
A survey was conducted among 125 students of class 10 studying in Gyan Mandir Secondary School regarding the places for educational tour and it was found that 65 students preferred to visit Lumbini (L), 75 preferred to visit Pokhara (P), and 25 preferred both the places.
- a)Write the cardinality of set of students who preferred to visit both Pokhara and Lumbini in set notational form.
- b)Show the above information in a Venn-diagram.
- c)Find the number of students who preferred neither of two places.
- d)Find the ratio of the number of students who preferred Lumbini only and Pokhara only.
Solution
Solution Part
Given
n(U) = 125; n(L) = 65; n(P) = 75; n(L ∩ P) = 25
The cardinality of set of students who preferred to visit both Pokhara and Lumbini is n(P ∩ L) = 25
Venn Diagram
no(L) = 40, n(L∩P) = 25, no(P) = 50, outside = 10
n(U) = 125, n(L) = 65, n(P) = 75, n(P ∩ L) = 25
n(P ∪ L) = n(P) + n(L) – n(P ∩ L)
= 75 + 65 – 25 = 115
= 75 + 65 – 25 = 115
n(P̄ ∪ L̄) = n(U) – n(P ∪ L) = 125 – 115 = 10
∴ 10 students preferred neither of two places.
No. of students who preferred Lumbini only,
no(L) = n(L) – n(P ∩ L) = 65 – 25 = 40
no(L) = n(L) – n(P ∩ L) = 65 – 25 = 40
No. of students who preferred Pokhara only,
no(P) = n(P) – n(P ∩ L) = 75 – 25 = 50
no(P) = n(P) – n(P ∩ L) = 75 – 25 = 50
So, the ratio of no(L) and no(P) = 40/50 = 4 : 5
Question
Complete Question
A survey was carried out in a village of Chandrapur municipality of Rautahat district regarding the local languages. Among 1,400 people participated in the survey, it was found that 600 people can speak Bhojpuri, 900 can speak Maithili and 350 people can speak Bhojpuri as well as Maithili languages.
- a)If B and M represent the sets of people who can speak Bhojpuri and Maithili respectively, write the cardinality of n(B ∩ M).
- b)Draw a Venn-diagram to show the above data.
- c)How many people cannot speak both the languages?
- d)How many more or less people can speak Maithili only than Bhojpuri only?
Solution
Solution Part
Given
n(U) = 1,400; n(B) = 600; n(M) = 900; n(B ∩ M) = 350
The cardinality of n(B ∩ M) = 350
Venn Diagram
no(B) = 250, n(B∩M) = 350, no(M) = 550, outside = 250
n(U) = 1400, n(B) = 600, n(M) = 900, n(B ∩ M) = 350
n(B ∪ M) = n(B) + n(M) – n(B ∩ M)
= 600 + 900 – 350 = 1150
= 600 + 900 – 350 = 1150
n(B̄ ∪ M̄) = n(U) – n(B ∪ M) = 1400 – 1150 = 250
∴ 250 people cannot speak both the languages.
No. of people can speak Bhojpuri only,
no(B) = n(B) – n(B ∩ M) = 600 – 350 = 250
no(B) = n(B) – n(B ∩ M) = 600 – 350 = 250
No. of people can speak Maithili only,
no(M) = n(M) – n(B ∩ M) = 900 – 350 = 550
no(M) = n(M) – n(B ∩ M) = 900 – 350 = 550
Difference of no(M) and no(B) = 550 – 250 = 300
∴ The number of people who can speak Maithili only is 300 more than the number of people who can speak Bhojpuri only.
Question
Complete Question
During 'Visit Nepal 2020', among 7,500 Chinese tourists who visited Nepal, 60% of them had already visited Bhutan, 50% had visited Sri Lanka, and 30% have visited both the countries.
- a)If B and S denote the sets of tourists who visited Bhutan and Sri Lanka respectively, write the number of tourists who visited Bhutan in set notation.
- b)Illustrate this information in a Venn-diagram.
- c)How many tourists have visited neither Bhutan nor Sri Lanka?
- d)How many tourists have already visited only one of these countries?
Solution
Solution Part
Given
n(U) = 7,500; n(B) = 60% of 7,500 = 4,500; n(S) = 50% of 7,500 = 3,750; n(B ∩ S) = 30% of 7,500 = 2,250
n(B) = 60% of 7500 = 4500
Venn Diagram
no(B)=2250, n(B∩S)=2250, no(S)=1500, outside=1500
n(U)=7500, n(B)=4500, n(S)=3750, n(B∩S)=2250
n(B ∪ S) = n(B) + n(S) – n(B ∩ S)
= 4500 + 3750 – 2250 = 6000
= 4500 + 3750 – 2250 = 6000
n(B̄ ∪ S̄) = n(U) – n(B ∪ S) = 7500 – 6000 = 1500
∴ 1500 tourists have visited neither Bhutan nor Sri Lanka.
no(B) = n(B) – n(B∩S) = 4500 – 2250 = 2250
no(S) = n(S) – n(B∩S) = 3750 – 2250 = 1500
No. who visited only one country = no(B) + no(S) = 2250 + 1500 = 3750
Question
Complete Question
In a survey conducted in a community of Gorkha district regarding cultural dances, it was found that out of 500 people, 180 people can perform Sorathi dance (S), 250 can perform Ghatu dance (G) and 120 can perform neither of these two dances.
- a)Write the set notation that represents the number of people who can perform neither Sorathi nor Ghatu dance.
- b)Represent the above information in a Venn-diagram.
- c)How many people can perform both the dances?
- d)Compare the number of people who can perform Sorathi only and Ghatu only.
Solution
Solution Part
Given
n(U) = 500; n(S) = 180; n(G) = 250; n((S ∪ G)̄) = 120
The set notation is n(S̄ ∪ Ḡ) = 120
Venn Diagram
no(S)=130, n(S∩G)=50, no(G)=200, outside=120
n(U)=500, n(S)=180, n(G)=250, n(S̄∪Ḡ)=120
Let n(S ∩ G) = x
n(U) = no(S) + no(G) + n(S∩G) + n(S̄∪Ḡ)
500 = (180–x) + (250–x) + x + 120
500 = 550 – x
x = 50
500 = (180–x) + (250–x) + x + 120
500 = 550 – x
x = 50
∴ 50 people can perform both the dances. 50
no(S) = 180 – 50 = 130
no(G) = 250 – 50 = 200
Difference = 200 – 130 = 70
∴ The number of people who can perform Sorathi only is 70 less than the number of people who can perform Ghatu only.
OR, Ratio of no(G) and no(S) = 130/200 = 13 : 20
Question
Complete Question
Last Wednesday, a School successfully accomplished its school's day. For this program, every student participated in at least one of the activities, athletics or music. In a class of 45 students, 21 participated in athletics (A) and 29 participated in music (M).
- a)Write the cardinality of n(Ā ∪ M̄)?
- b)Draw a Venn-diagram to represent the above information.
- c)How many students participated in both the activities?
- d)Compare the number of students who participated in athletics only and music only.
Solution
Solution Part
Given
n(U) = 45; n(A) = 21; n(M) = 29; n((A ∪ M)̄) = 0
Since every student participated in at least one activity, n(Ā ∪ M̄) = 0
Venn Diagram
no(A)=16, n(A∩M)=5, no(M)=24 (no outside region since n(Ā∪M̄)=0)
n(U)=45, n(A)=21, n(M)=29, n(Ā∪M̄)=0
Let n(A ∩ M) = x
n(U) = no(A) + no(M) + n(A∩M) + n(Ā∪M̄)
45 = (21–x) + (29–x) + x + 0
45 = 50 – x ⟹ x = 5
45 = (21–x) + (29–x) + x + 0
45 = 50 – x ⟹ x = 5
∴ 5 students participated in both the activities. 5
no(A) = 21 – 5 = 16
no(M) = 29 – 5 = 24
Difference = 24 – 16 = 8
∴ The number of students who participated in music only is 8 more than the number of students who participated in athletics only.
OR, Ratio of no(A) and no(M) = 16/24 = 2 : 3
Question
Complete Question
In a survey conducted among 150 students of a school, it was found that 70 students liked cricket, 62 liked basketball and 30 students did not like any of these two games.
- a)If C and B denote the set of students who liked cricket and basketball respectively, write the cardinality of n(B̄ ∪ C̄).
- b)Present the information in a Venn-diagram.
- c)Find the number of students who liked cricket only.
- d)Compare the number of students who liked both games and who liked except these two games.
Solution
Solution Part
Given
n(U) = 150; n(C) = 70; n(B) = 62; n((C ∪ B)̄) = 30
The cardinality of n(B̄ ∪ C̄) = 30
Venn Diagram
no(B)=50, n(B∩C)=12, no(C)=58, outside=30
n(U)=150, n(C)=70, n(B)=62, n(B̄∪C̄)=30
Let n(B ∩ C) = x
n(U) = no(B) + no(C) + n(B∩C) + n(B̄∪C̄)
150 = (62–x) + (70–x) + x + 30
150 = 162 – x ⟹ x = 12
150 = (62–x) + (70–x) + x + 30
150 = 162 – x ⟹ x = 12
No. of students who liked cricket only = no(C) = 70 – 12 = 58
n(B ∩ C) = 12, n(B̄ ∪ C̄) = 30
Difference = n(B̄ ∪ C̄) – n(B∩C) = 30 – 12 = 18
∴ The number of students who liked both games is 18 less than the number of students who liked except these two games.
OR, Ratio of n(B∩C) and n(B̄∪C̄) = 12/30 = 2 : 5
Question
Complete Question
Among 54 SEE appeared students from a school, 18 students got 'A+' grade in Mathematics only, 25 got 'A+' grade in English only and 7 students did not get 'A+' grade in these two subjects.
- a)Write the cardinalities of the given sets in set notational forms.
- b)Show the above information in Venn-diagram.
- c)How many students got 'A+' grade in Mathematics?
- d)How many more or less students got 'A+' grade not in English than not in Mathematics?
Solution
Solution Part
Given
n(U) = 54; n₀(M) = 18; n₀(E) = 25; n((M ∪ E)̄) = 7
Let M and E denote the sets of students who got 'A+' grade in Mathematics and English respectively.
n(U) = 54, no(M) = 18, no(E) = 25, n(M̄ ∪ Ē) = 7
Venn Diagram
no(M)=18, n(M∩E)=4, no(E)=25, outside=7
n(U)=54, no(M)=18, no(E)=25, n(M̄∪Ē)=7
Let n(M ∩ E) = x
n(U) = no(M) + no(E) + n(M∩E) + n(M̄∪Ē)
54 = 18 + 25 + x + 7
54 = 50 + x ⟹ x = 4
54 = 18 + 25 + x + 7
54 = 50 + x ⟹ x = 4
n(M) = no(M) + n(M∩E) = 18 + 4 = 22
n(E) = no(E) + n(M∩E) = 25 + 4 = 29
n(Ē) = n(U) – n(E) = 54 – 29 = 25
n(M̄) = n(U) – n(M) = 54 – 22 = 32
Difference = 32 – 25 = 7
∴ Students who got 'A+' not in English is 7 less than students who got 'A+' not in Mathematics.
Question
Complete Question
In a survey of a group of people, 20% are using cellular data but not Wi-Fi, 65% are using Wi-Fi but not cellular data and 5% of them use neither cellular data nor Wi-Fi.
- a)If C and W denote the sets of people who are using cellular data and Wi-Fi respectively, write the cardinality of n(C̄ ∪ W̄).
- b)Represent the above information in a Venn-diagram.
- c)Find the percent of people who are using Wi-Fi.
- d)By what percent of the people who are not using cellular data is more or less than the people who are not using Wi-Fi?
Solution
Solution Part
Given
Taking n(U) = 100%: n₀(C) = 20%; n₀(W) = 65%; n((C ∪ W)̄) = 5%
The cardinality of n(C̄ ∪ W̄) = 5
Venn Diagram (let n(U) = 100)
no(C)=20, n(C∩W)=10, no(W)=65, outside=5
Let n(U)=100. no(C)=20, no(W)=65, n(C̄∪W̄)=5
Let n(C ∩ W) = x
n(U) = no(C) + no(W) + n(C∩W) + n(C̄∪W̄)
100 = 20 + 65 + x + 5 = 90 + x ⟹ x = 10
100 = 20 + 65 + x + 5 = 90 + x ⟹ x = 10
n(W) = no(W) + n(C∩W) = 65 + 10 = 75%
n(C) = 20 + 10 = 30%, n(C̄) = 100 – 30 = 70%
n(W) = 75%, n(W̄) = 100 – 75 = 25%
Difference = 70 – 25 = 45%
∴ The percent of people who are not using cellular data is 45% more than the people who are not using Wi-Fi.
Question
Complete Question
In a survey of a group of people, it was found that 65% of them liked comedy movies, 63% liked action movies, 33% liked both types of movies, and 150 people did not like both types of movies.
- a)Draw a Venn-diagram to illustrate the above information.
- b)Find the number of people participated in the survey.
- c)Find the number of people who liked both types of movies.
- d)Amrita calculated that the number of people who did not like comedy movie is 150 more than the number of people who liked action movie only. Justify her calculation.
Solution
Solution Part
Given
Let n(U) = x: n(C) = 0.65x; n(A) = 0.63x; n(C ∩ A) = 0.33x; n((C ∪ A)̄) = 150
Venn Diagram (let n(U) = x)
n(C)=0.65x, n(A)=0.63x, n(C∩A)=0.33x, n(C̄∪Ā)=150
n(U) = no(C) + no(A) + n(C∩A) + n(C̄∪Ā)
x = 0.32x + 0.30x + 0.33x + 150
x = 0.95x + 150
0.05x = 150 ⟹ x = 3000
x = 0.32x + 0.30x + 0.33x + 150
x = 0.95x + 150
0.05x = 150 ⟹ x = 3000
∴ 3000 people participated in the survey.
n(C ∩ A) = 0.33 × 3000 = 990
n(C̄) = n(U) – n(C) = 3000 – 0.65×3000 = 3000 – 1950 = 1050
no(A) = 0.30 × 3000 = 900
Difference = 1050 – 900 = 150
∴ Amrita's calculation is correct.
Question
Complete Question
In an examination, 80% examinees passed in English, 70% in Mathematics, 60% passed in both the subjects, and 45 examinees failed in both subjects.
- a)Draw a Venn-diagram to represent the above information.
- b)Find the number of examinees participated in the survey.
- c)Find the number of examinees who passed in both subjects.
- d)Ram calculated that the number of examinees who failed in English is double the number of examinees who passed mathematics only. State whether he is right or wrong by testing his calculation.
Solution
Solution Part
Given
Let n(U) = x: n(E) = 0.80x; n(M) = 0.70x; n(E ∩ M) = 0.60x; n((E ∪ M)̄) = 45
Venn Diagram (let n(U) = x)
n(E)=0.8x, n(M)=0.7x, n(E∩M)=0.6x, n(Ē∪M̄)=45
x = 0.2x + 0.1x + 0.6x + 45
x = 0.9x + 45
0.1x = 45 ⟹ x = 450
x = 0.9x + 45
0.1x = 45 ⟹ x = 450
∴ 450 examinees participated in the survey.
n(E ∩ M) = 0.6 × 450 = 270
n(Ē) = n(U) – n(E) = 450 – 0.8×450 = 450 – 360 = 90
no(M) = 0.1 × 450 = 45
n(Ē) / no(M) = 90/45 = 2 ∴ n(Ē) = 2 × no(M)
∴ Ram's calculation is correct. ✓
Question
Complete Question
In a survey of a community, it was found that 65% of people liked folk songs, 55% liked modern songs and 10% of people did not like both types of songs.
- a)Illustrate the above information in a Venn-diagram.
- b)What percentage of people liked either folk songs or modern songs?
- c)If 360 people liked both types of songs, how many people were surveyed?
- d)How many times is the number of people who liked both types of songs of the number of people who did not like both types of songs?
Solution
Solution Part
Given
Taking n(U) = 100%: n(F) = 65%; n(M) = 55%; n((F ∪ M)̄) = 10%
Venn Diagram (let n(U) = 100)
no(F)=35, n(F∩M)=30, no(M)=25, outside=10
n(F ∪ M) = n(U) – n(F̄ ∪ M̄) = 100 – 10 = 90%
∴ 90% people liked either folk songs or modern songs.
n(U)=100. n(F)=65, n(M)=55, n(F̄∪M̄)=10
Let n(F ∩ M) = x
100 = (65–x) + (55–x) + x + 10
100 = 130 – x ⟹ x = 30
100 = 130 – x ⟹ x = 30
So 30% liked both. Let total = y.
30% of y = 360 ⟹ y = 1200 people were surveyed.
n(F ∩ M) = 360
n(F̄ ∪ M̄) = 10% of 1200 = 120
360 ÷ 120 = 3 times
∴ The number who liked both is 3 times the number who did not like both.
Question
Complete Question
In a survey of some farmers in a community, 70% of them are found cultivating rice, 60% cultivating wheat, 20% are not cultivating both the crops, and 450 farmers are found cultivating both the crops.
- a)Draw a Venn-diagram to illustrate the above information.
- b)Find the percentage of farmers who are cultivating either rice or wheat.
- c)Find the total number of farmers participated in the survey.
- d)By how many times is the number of farmers who are cultivating both the crops more than the number of farmers who are cultivating none of these crops?
Solution
Solution Part
Given
Let n(U) = x: n(R) = 0.70x; n(W) = 0.60x; n((R ∪ W)̄) = 0.20x; n(R ∩ W) = 450
Venn Diagram (let n(U) = 100)
no(R)=20, n(R∩W)=50, no(W)=10, outside=20
n(R ∪ W) = n(U) – n(R̄ ∪ W̄) = 100 – 20 = 80%
Let n(R ∩ W) = x
100 = (70–x) + (60–x) + x + 20
100 = 150 – x ⟹ x = 50
100 = 150 – x ⟹ x = 50
So 50% cultivate both. Let total = y.
50% of y = 450 ⟹ y = 900 farmers
n(R ∩ W) = 450
n(R̄ ∪ W̄) = 20% of 900 = 180
450 ÷ 180 = 2.5 times
∴ The number cultivating both is 2.5 times the number cultivating none.
Question
Complete Question
In a survey of 200 people, it was found that 100 people drink tea, 70 drink coffee and 40 drink both tea and coffee.
- a)If T and C denote the sets of people who drink tea and coffee respectively, write the values of n(T), n(C) and n(T ∩ C).
- b)Show the above information in a Venn-diagram.
- c)Find the number of people who drink neither tea nor coffee.
- d)Find the ratio of people who drink tea only to those who drink coffee only.
Solution
Solution Part
Given
n(U) = 200; n(T) = 100; n(C) = 70; n(T ∩ C) = 40
n(U) = 200, n(T) = 100, n(C) = 70, n(T ∩ C) = 40
Venn Diagram
no(T)=60, n(T∩C)=40, no(C)=30, outside=70
n(U)=200, n(T)=100, n(C)=70, n(T∩C)=40
n(T ∪ C) = n(T) + n(C) – n(T ∩ C)
= 100 + 70 – 40 = 130
= 100 + 70 – 40 = 130
n(T̄ ∪ C̄) = n(U) – n(T ∪ C) = 200 – 130 = 70
∴ 70 people drink neither tea nor coffee.
no(T) = n(T) – n(T∩C) = 100 – 40 = 60
no(C) = n(C) – n(T∩C) = 70 – 40 = 30
Ratio = no(T) : no(C) = 60 : 30 = 2 : 1
Question
Complete Question
In a survey of 1000 people, it was found that 600 read English newspaper (E), 500 read Nepali newspaper (N) and 200 read both English and Nepali newspapers.
- a)Write the cardinality of n(E ∩ N).
- b)Draw a Venn-diagram to represent the above information.
- c)Find the number of people who read neither English nor Nepali newspaper.
- d)How many more people read English newspaper only than Nepali newspaper only?
Solution
Solution Part
Given
n(U) = 1,000; n(E) = 600; n(N) = 500; n(E ∩ N) = 200
n(E ∩ N) = 200
Venn Diagram
no(E)=400, n(E∩N)=200, no(N)=300, outside=100
n(U)=1000, n(E)=600, n(N)=500, n(E∩N)=200
n(E ∪ N) = n(E) + n(N) – n(E ∩ N)
= 600 + 500 – 200 = 900
= 600 + 500 – 200 = 900
n(Ē ∪ N̄) = n(U) – n(E ∪ N) = 1000 – 900 = 100
∴ 100 people read neither English nor Nepali newspaper.
no(E) = n(E) – n(E∩N) = 600 – 200 = 400
no(N) = n(N) – n(E∩N) = 500 – 200 = 300
Difference = 400 – 300 = 100
∴ 100 more people read English newspaper only than Nepali newspaper only.
Question
Complete Question
In a class of 40 students, 25 like Science (S), 20 like Mathematics (M) and 10 like both Science and Mathematics.
- a)Write the cardinality of n(S ∩ M).
- b)Represent the above data in a Venn-diagram.
- c)Find the number of students who like neither Science nor Mathematics.
- d)Find the number of students who like Science only.
Solution
Solution Part
Given
n(U) = 40; n(S) = 25; n(M) = 20; n(S ∩ M) = 10
n(S ∩ M) = 10
Venn Diagram
no(S)=15, n(S∩M)=10, no(M)=10, outside=5
n(U)=40, n(S)=25, n(M)=20, n(S∩M)=10
n(S ∪ M) = n(S) + n(M) – n(S ∩ M)
= 25 + 20 – 10 = 35
= 25 + 20 – 10 = 35
n(S̄ ∪ M̄) = n(U) – n(S ∪ M) = 40 – 35 = 5
∴ 5 students like neither Science nor Mathematics.
no(S) = n(S) – n(S ∩ M) = 25 – 10 = 15
∴ 15 students like Science only.
Question
Complete Question
In a survey of 500 students, 300 play football (F), 270 play volleyball (V) and 100 play neither of these two games.
- a)Write the value of n(F̄ ∪ V̄) in set notation.
- b)Represent the above information in a Venn-diagram.
- c)Find the number of students who play both football and volleyball.
- d)Find the number of students who play football only.
Solution
Solution Part
Given
n(U) = 500; n(F) = 300; n(V) = 270; n((F ∪ V)̄) = 100
n(F̄ ∪ V̄) = 100
Venn Diagram
no(F)=230, n(F∩V)=70, no(V)=200, outside=100
n(U)=500, n(F)=300, n(V)=270, n(F̄∪V̄)=100
Let n(F ∩ V) = x
n(U) = no(F) + no(V) + n(F∩V) + n(F̄∪V̄)
500 = (300–x) + (270–x) + x + 100
500 = 670 – x ⟹ x = 170
500 = (300–x) + (270–x) + x + 100
500 = 670 – x ⟹ x = 170
∴ 170 students play both football and volleyball.
no(F) = n(F) – n(F∩V) = 300 – 170 = 130
∴ 130 students play football only.
Extra Question Placeholders
Five ready-to-edit templates for additional two-set problems.
Question
Complete Question
Write the full word-problem statement here, including the universal set and information about both sets.
- a)Write sub-question (a) here.
- b)Write sub-question (b) here.
- c)Write sub-question (c) here.
- d)Write sub-question (d) here.
Solution
Solution Part
Given
n(U) = ____; n(A) = ____; n(B) = ____; n(A ∩ B) = ____; n((A ∪ B)̄) = ____
Write the solution for part a) here.
Write the solution for part b) here.
Write the solution for part c) here.
Write the solution for part d) here.
Question
Complete Question
Write the full word-problem statement here, including the universal set and information about both sets.
- a)Write sub-question (a) here.
- b)Write sub-question (b) here.
- c)Write sub-question (c) here.
- d)Write sub-question (d) here.
Solution
Solution Part
Given
n(U) = ____; n(A) = ____; n(B) = ____; n(A ∩ B) = ____; n((A ∪ B)̄) = ____
Write the solution for part a) here.
Write the solution for part b) here.
Write the solution for part c) here.
Write the solution for part d) here.
Question
Complete Question
Write the full word-problem statement here, including the universal set and information about both sets.
- a)Write sub-question (a) here.
- b)Write sub-question (b) here.
- c)Write sub-question (c) here.
- d)Write sub-question (d) here.
Solution
Solution Part
Given
n(U) = ____; n(A) = ____; n(B) = ____; n(A ∩ B) = ____; n((A ∪ B)̄) = ____
Write the solution for part a) here.
Write the solution for part b) here.
Write the solution for part c) here.
Write the solution for part d) here.
Question
Complete Question
Write the full word-problem statement here, including the universal set and information about both sets.
- a)Write sub-question (a) here.
- b)Write sub-question (b) here.
- c)Write sub-question (c) here.
- d)Write sub-question (d) here.
Solution
Solution Part
Given
n(U) = ____; n(A) = ____; n(B) = ____; n(A ∩ B) = ____; n((A ∪ B)̄) = ____
Write the solution for part a) here.
Write the solution for part b) here.
Write the solution for part c) here.
Write the solution for part d) here.
Question
Complete Question
Write the full word-problem statement here, including the universal set and information about both sets.
- a)Write sub-question (a) here.
- b)Write sub-question (b) here.
- c)Write sub-question (c) here.
- d)Write sub-question (d) here.
Solution
Solution Part
Given
n(U) = ____; n(A) = ____; n(B) = ____; n(A ∩ B) = ____; n((A ∪ B)̄) = ____
Write the solution for part a) here.
Write the solution for part b) here.
Write the solution for part c) here.
Write the solution for part d) here.