# Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 1 - Sets and Relations [Latest edition]

## Chapter 1: Sets and Relations

Exercise 1.1Exercise 1.2Miscellaneous Exercise 1
Exercise 1.1 [Pages 9 - 10]

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 1 Sets and Relations Exercise 1.1 [Pages 9 - 10]

Exercise 1.1 | Q 1. (i) | Page 9

Describe the following set in the Roster Form:

{x/x is a letter of the word "MARRIAGE"}

Exercise 1.1 | Q 1. (ii) | Page 9

Describe the following set in the Roster Form:

{x/x "is an integer", -1/2< x < 9/2}

Exercise 1.1 | Q 1. (iii) | Page 9

Describe the following set in the Roster Form:

{x/x = 2n, n ∈ N}

Exercise 1.1 | Q 2. (i) | Page 9

Describe the following set in the Set-Builder form:

{0}

Exercise 1.1 | Q 2. (ii) | Page 9

Describe the following set in the Set-Builder form:

{0, ±1, ±2, ±3}

Exercise 1.1 | Q 2. (iii) | Page 9

Describe the following set in the Set-Builder form:

{1/2 , 2/5 , 3/10 , 4/17 , 5/26 , 6/37 , 7/50}

Exercise 1.1 | Q 3. (i) | Page 9

If A = {x/6x2 + x - 15 = 0}

B = {x/2x2 - 5x - 3 = 0}

C = {x/2x2 - x - 3 = 0} then

find (A ∪ B ∪ C)

Exercise 1.1 | Q 3. (ii) | Page 9

If A = {x/6x2 + x - 15 = 0}

B = {x/2x2 - 5x - 3 = 0}

C = {x/2x2 - x - 3 = 0} then

find (A ∩ B ∩ C)

Exercise 1.1 | Q 4 | Page 9

If A, B, C are the sets for the letters in the words 'college', 'marriage' and 'luggage' respectively, then verify that
A - (B ∪ C) = (A - B) ∩ (A - C)

Exercise 1.1 | Q 5. (i) | Page 10

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Exercise 1.1 | Q 5. (ii) | Page 10

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
A∩(B∪C) = (A∩B) ∪ (A∩C)

Exercise 1.1 | Q 5. (iii) | Page 10

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
(A ∪ B)' = (A' ∩ B')

Exercise 1.1 | Q 5. (iv) | Page 10

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
(A ∩ B)' = A' ∪ B'

Exercise 1.1 | Q 5. (v) | Page 10

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
A = (A ∩ B) ∪ (A ∩ B')

Exercise 1.1 | Q 5. (vi) | Page 10

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
B = (A ∩ B) ∪ (A'∩ B)

Exercise 1.1 | Q 5. (vii) | Page 10

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
n (A ∪ B) = n(A) + n(B) – n(A ∩ B)

Exercise 1.1 | Q 6. (i) | Page 10

If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A'∩ B') = 5, find: n(A ∪ B)

Exercise 1.1 | Q 6. (ii) | Page 10

If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A'∩B') = 5, find: n(A ∩ B)

Exercise 1.1 | Q 6. (iii) | Page 10

If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A' ∩ B') = 5, find: n(A' ∩ B)

Exercise 1.1 | Q 6. (iv) | Page 10

If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A' ∩ B') = 5,  find: n(A ∩ B')

Exercise 1.1 | Q 7. (i) | Page 10

Out of 200 students; 35 students failed in MHT-CET, 40 in AIEEE and 40 in IIT entrance, 20 failed in MHT-CET and AIEEE, 17 in AIEEE and IIT entrance, 15 in MHT-CET and IIT entrance, and 5 failed in all three examinations. Find how many students : did not fail in any examination.

Exercise 1.1 | Q 7. (ii) | Page 10

Out of 200 students; 35 students failed in MHT-CET, 40 in AIEEE and 40 in IIT entrance, 20 failed in MHT-CET and AIEEE, 17 in AIEEE and IIT entrance, 15 in MHT-CET and IIT entrance, and 5 failed in all three examinations. Find how many students : failed in AIEEE or IIT entrance.

Exercise 1.1 | Q 8 | Page 10

From amongst 2000 literate individuals of a town, 70% read Marathi newspapers, 50% read English newspapers and 32.5% read both Marathi and English newspapers. Find the number of individuals who read

1. at least one of the newspapers.
2. neither Marathi nor English newspaper.
3. Only one of the newspapers.
Exercise 1.1 | Q 9 | Page 10

In a hostel, 25 students take tea, 20 students take coffee, 15 students take milk, 10 students take both tea and coffee, 8 students take both milk and coffee. None of them take tea and milk both and everyone takes at least one beverage, find the number of students in the hostel.

Exercise 1.1 | Q 10. (i) | Page 10

There are 260 persons with skin disorders. If 150 had been exposed to the chemical A, 74 to the chemical B, and 36 to both chemicals A and B, find the number of persons exposed to Chemical A but not Chemical B.

Exercise 1.1 | Q 10. (ii) | Page 10

There are 260 persons with skin disorders. If 150 had been exposed to the chemical A, 74 to the chemical B, and 36 to both chemicals A and B, find the number of persons exposed to Chemical B but not Chemical A.

Exercise 1.1 | Q 10. (iii) | Page 10

There are 260 persons with skin disorders. If 150 had been exposed to the chemical A, 74 to the chemical B, and 36 to both chemicals A and B, find the number of persons exposed to Chemical A or Chemical B.

Exercise 1.1 | Q 11 | Page 10

If A = {1,2,3} write the set of all possible subsets of A.

Exercise 1.1 | Q 12. (i) | Page 10

Write the following interval in the set-builder form (– 3, 0).

Exercise 1.1 | Q 12. (ii) | Page 10

Write the following interval in the set-builder form: [6,12]

Exercise 1.1 | Q 12. (iii) | Page 10

Write the following interval in the set-builder form: (6, 12)

Exercise 1.1 | Q 12. (iv) | Page 10

Write the following interval in the set-builder form: (-23, 5)

Exercise 1.2 [Pages 15 - 16]

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 1 Sets and Relations Exercise 1.2 [Pages 15 - 16]

Exercise 1.2 | Q 1 | Page 15

If (x – 1, y + 4) = (1, 2) find the values of x and y.

Exercise 1.2 | Q 2 | Page 15

If (x + 1/3, y/3 - 1) = (1/3 , 3/2), find x and y.

Exercise 1.2 | Q 3. (i) | Page 15

If A = {a, b, c}, B = (x , y} find A × B.

Exercise 1.2 | Q 3. (ii) | Page 15

If A = {a, b, c}, B = (x , y} find B × A.

Exercise 1.2 | Q 3. (iii) | Page 15

If A = {a, b, c}, B = (x , y} find A × A.

Exercise 1.2 | Q 3. (iv) | Page 15

If A = {a, b, c}, B = (x , y} find B × B.

Exercise 1.2 | Q 4 | Page 15

If P = {1, 2, 3} and Q = {6, 4}, find the sets P × Q and Q × P.

Exercise 1.2 | Q 5. (i) | Page 16

Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find A × (B ∩ C).

Exercise 1.2 | Q 5. (ii) | Page 16

Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6} Find (A × B) ∩ (A × C).

Exercise 1.2 | Q 5. (iii) | Page 16

Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find A × (B ∪ C).

Exercise 1.2 | Q 5. (iv) | Page 16

Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find (A × B) ∪ (A × C).

Exercise 1.2 | Q 6 | Page 16

Express {(x, y) / x2 +y2 = 100 where x, y ∈ W} as a set of ordered pairs.

Exercise 1.2 | Q 7. (i) | Page 16

Write the domain and range of the following relation: {(a, b) / a ∈ N, a < 6 and b = 4}

Exercise 1.2 | Q 7. (ii) | Page 16

Write the domain and range of the following relation: {(a, b) / a, b ∈ N, a + b = 12}

Exercise 1.2 | Q 7. (iii) | Page 16

Write the domain and range of the following relation: (2, 4), (2, 5), (2,6), (2, 7)}

Exercise 1.2 | Q 8 | Page 16

Let A = {6, 8} and B = {1, 3, 5}.
Let R = {(a, b)/a∈ A, b∈ B, a – b is an even number}. Show that R is an empty relation from A to B.

Exercise 1.2 | Q 9. (i) | Page 16

Write the relation in the Roster form and hence find its domain and range :
R1 = {(a, a2) / a is prime number less than 15}

Exercise 1.2 | Q 9. (ii) | Page 16

Write the relation in the Roster form and hence find its domain and range:

R2 = {("a", 1/"a")  "/"  0 < "a" ≤ 5, "a" ∈ "N"}

Exercise 1.2 | Q 10 | Page 16

R = {(a, b) / b = a + 1, a ∈ Z, 0 < a < 5}. Find the Range of R.

Exercise 1.2 | Q 11. (i) | Page 16

Find the following relation as sets of ordered pairs:
{(x, y) / y = 3x, x ∈ {1, 2, 3}, y ∈ {3, 6, 9, 12}}

Exercise 1.2 | Q 11. (ii) | Page 16

Find the following relation as sets of ordered pairs:
{(x, y) / y > x + 1, x ∈ {1, 2} and y ∈ {2, 4, 6}}

Exercise 1.2 | Q 11. (iii) | Page 16

Find the following relation as sets of ordered pairs:
{(x, y) / x + y = 3, x, y ∈ {0, 1, 2, 3}}

Miscellaneous Exercise 1 [Pages 16 - 17]

### Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board Chapter 1 Sets and Relations Miscellaneous Exercise 1 [Pages 16 - 17]

Miscellaneous Exercise 1 | Q 1. (i) | Page 16

Write the following set in the set-builder form:

{10, 20, 30, 40, 50}

Miscellaneous Exercise 1 | Q 1. (ii) | Page 16

Write the following set in the set-builder form:

{a, e, i, o, u)

Miscellaneous Exercise 1 | Q 1. (iii) | Page 16

Write the following set in the set-builder form:

{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

Miscellaneous Exercise 1 | Q 2. (i) | Page 17

If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write the set: A ∪ B.

Miscellaneous Exercise 1 | Q 2. (ii) | Page 17

If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write the set: B ∩ C.

Miscellaneous Exercise 1 | Q 2. (iii) | Page 17

If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write the set: A – B

Miscellaneous Exercise 1 | Q 2. (iv) | Page 17

If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write the set: B – C

Miscellaneous Exercise 1 | Q 2. (v) | Page 17

If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write the set: A ∪ B ∪ C.

Miscellaneous Exercise 1 | Q 2. (vi) | Page 17

If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write the set: A ∩ (B ∪ C).

Miscellaneous Exercise 1 | Q 3 | Page 17

In a survey of 425 students in a school, it was found that 115 drink apple juice, 160 drink orange juice, and 80 drink both apple as well as orange juice. How many drinks neither apple juice nor orange juice?

Miscellaneous Exercise 1 | Q 4 | Page 17

In a school there are 20 teachers who teach Mathematics or Physics, of these, 12 teach Mathematics and 4 teach both Physics and Mathematics. How many teachers teach Physics?

Miscellaneous Exercise 1 | Q 5. (i) | Page 17

If A = {1, 2, 3} and B = {2, 4}, state the elements of A × A, A × B, B × A, B × B, (A × B) ∩ (B × A).

Miscellaneous Exercise 1 | Q 5. (ii) | Page 17

If A = {– 1, 1}, find A × A × A.

Miscellaneous Exercise 1 | Q 6. (i) | Page 17

If A = {1, 2, 3}, B = {4, 5, 6} which of following are relation from A to B : R1 = {(1, 4), (1, 5), (1, 6)}

Miscellaneous Exercise 1 | Q 6. (ii) | Page 17

If A = {1, 2, 3}, B = {4, 5, 6} which of following are relation from A to B : R2 = {(1, 5), (2, 4), (3, 6)}

Miscellaneous Exercise 1 | Q 6. (iii) | Page 17

If A = {1, 2, 3}, B = {4, 5, 6} which of following are relation from A to B : R3 = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}

Miscellaneous Exercise 1 | Q 6. (iv) | Page 17

If A = {1, 2, 3}, B = {4, 5, 6} which of following are relation from A to B : R4 = {(4, 2), (2, 6), (5, 1), (2, 4)}

Miscellaneous Exercise 1 | Q 7 | Page 17

Determine the Domain and Range of the following relations : R = {(a, b) / a ∈ N, a < 5, b = 4}

## Chapter 1: Sets and Relations

Exercise 1.1Exercise 1.2Miscellaneous Exercise 1

## Balbharati solutions for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 1 - Sets and Relations

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