Practice Set 1.4 Algebra 9th Std Maths Part 1 Answers Chapter 1 Sets
ii. n(T ∪ C) = n(T) + n(C) – n(T ∩ C)
= 80 + 60 – 20
∴ n(T ∪ C) = 120
∴ 120 students drink tea or coffee
Also, there are 125 students in the hostel.
iii. Number of students who do not drink tea or coffee = n(U) – n(T ∪ C)
= 125 – 120
= 5
∴ 5 students do not drink tea or coffee.
Alternate Method:
Let U be the set of students in the hostel, T be the set of students who drink tea and C be the set of students who drink coffee.
From Venn diagram,
Student who drinks tea or coffee = n(T ∪ C) = 60 + 20 + 40 = 120
∴ The number of students who do not drink tea or coffee = n(U) – n(T ∪ C)
= 125 – 120 = 5
∴ 5 students do not drink tea or coffee.
Alternate Method:
Let U be the set of students who appeared for the exam,
E be the set of students who passed in English and M be the set of students who passed in Maths.
Since, none of the students failed in both subjects
∴ Total student = n(E ∪M)
= 10 + 40 + 20
= 70
∴ The number of students who passed at least in one of the subjects is 70.
ii. n(R ∪ S)=n (R) + n (S) – n (R ∩ S)
= 130 + 180 – 110
∴n (R ∪ S) = 200
∴ 200 students follow the hobby of rock climbing or sky watching.
iii. Total number of students = 220.
Number of students who do not follow the hobby of rock climbing or sky watching
= n (U) – n (R ∪ S)
= 220 – 200
= 20
iv. Number of students who follow the hobby of rock climbing only
= n (R) – n(R ∩ S)
= 130 – 110
= 20
v. Number of students who follow the hobby of sky watching only
= n (S) – n (R ∩ S)
= 180 – 110
= 70
Alternate Method:
Let U be the set of students of class IX,
R be the set of students who follow the hobby of rock climbing and
S be the set of students who follow the hobby of sky watching.
From the Venn diagram
i. Students who follow the hobby of rock climbing or sky watching
= n(R ∪ S)
= 20 + 110 + 70
= 200
ii. Number of students who do not follow the hobby of rock climbing or sky watching
= n (U) – n(R ∪S)
= 220 – 200
= 20
iii. Number of students who follow the hobby of rock climbing only
= n (R) – n(R ∩S)
= 130 – 110
= 20
iv. Number of students who follow the hobby of sky watching only
= n (S) – n (R ∩ S)
= 180 – 110
= 70
Question 1
Maharashtra Board Solution
Take different examples of sets and verify the above mentioned properties. (Textbook pg.no. 12)
Solution & Step-by-Step Answer:
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Solution & Step-by-Step Answer:
i. Let A = {3, 5}, B= {3, 5, 8, 9, 10} A ∩ B = B ∩ A = {3, 5}
ii. Let A = {3, 5}, B = {3, 5, 8, 9, 10} iii. Let A = {2, 3, 8, 10}, B = {3,8} iv. Let A = {2, 3, 8, 10}, B = {3, 8}, A ∩B = {3, 8} v. Let U= {3, 4, 6, 8}, A = {6, 4} vi. A ∩ φ = { } = φ vii. Let A = {6, 4}
Question 2
Maharashtra Board Solution
Observe the set A, B, C given by Venn diagrams and write which of these are disjoint sets. (Textbook pg. no. 12)
Solution & Step-by-Step Answer:
Here, A = {1, 2, 3, 4, 5, 6, 7} B = {3, 6, 8, 9, 10, 11, 12} C = {10, 11, 12} Now, A ∩ C = φ ∴ A and C are disjoint sets.
Question 3
Maharashtra Board Solution
Let the set of English alphabets be the Universal set. The letters of the word ‘LAUGH’ is one set and the letter of the word ‘CRY’ is another set. Can we say that these are two disjoint sets? Observe that intersection of these two sets is empty. (Textbook pg. no. 13)
Solution & Step-by-Step Answer:
Let A = {L, A, U, G, H} B = {C, R, Y} Now, A ∩ B = φ ∴ A and B are disjoint sets.
Question 4
Maharashtra Board Solution
Fill in the blanks with elements of that set. U = {1, 3, 5, 8, 9, 10, 11, 12, 13, 15} A = {1,11, 13} B = {8,5, 10, 11, 15} A’ = { } B’ = { } A ∩ B = { } A’ ∩ B’ = { } A ∪ B = { } A’ ∪ B’= { } (A ∩ B)’ = { } (A ∪ B)’ = { } Verify: (A ∩ B)’ = A’ u B’, (A u B)’ = A’ ∩ B’ (Textbook pg. no, 18)
Solution & Step-by-Step Answer:
U = {1, 3, 5, 8, 9, 10, 11, 12, 13, 15} A = {1, 11, 13} B = {8, 5, 10, 11, 15} A’ = {3, 5, 8, 9, 10, 12, 15} B’ = {1, 3, 9, 12, 13} A∩ B= {11} A’ ∩ B’= {3, 9, 12} …(i) A ∪ B = {1, 5, 8, 10, 11, 13, 15} A’ ∪ B’ = { 1, 3, 5, 8, 9, 10, 12, 13, 15} …(ii) (A ∩ B)’= { 1, 3, 5, 8, 9, 10, 12, 13,15} …(iii) (A ∪ B)’ = {3, 9, 12},..(iv) (A ∩ B)’ = A’ ∪ B’ … [From (ii) and (iii)] (A ∪ B)’ = A’ ∩ B’ … [From (i) and (iv)]
Question 5
Maharashtra Board Solution
A = {1,2,3, 5, 7,9,11,13} B = {1,2,4, 6, 8,12,13} Verify the above rule for the given set A and set B. (Textbook pg. no. 14)
Solution & Step-by-Step Answer:
A = {1, 2, 3, 5, 7, 9, 11, 13} B = {1, 2, 4, 6, 8, 12, 13} A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13} A ∩ B= {1, 2, 13} n(A) = 8, n(B) = 7, n(A ∪ B) = 12, n(A ∩ B) = 3 n(A ∩ B) = 12 …(i) n(A) + n(B) – n(A ∩ B) = 8 + 7 – 3 = 12 …(ii) ∴ n(A ∪ B) = n(A) + n(B) – n(A ∩ B) … [From (i) and (ii)]
Question 6
Maharashtra Board Solution
Verify the above rule for the given Venn diagram. (Textbook pg. no. 14)
Solution & Step-by-Step Answer:
n(A) = 5, n(B) = 6 n(A ∪ B) = 9, n(A ∩ B) = 2 Now, n(A ∪ B) = 9 …(i) n(A) + n(B) – n(A ∩ B) = 5 + 6 – 2 = 9 …(ii) ∴ n(A ∪ B) = n(A) + n(B) – n(A ∩ B). …[From (i) and (ii)]
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