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## Solutions for Chapter 1: Sets and Relations

Below listed, you can find solutions for Chapter 1 of Maharashtra State Board Balbharati for Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board.

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

**Describe the following set in the Roster Form:**

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

**Describe the following set in the Roster Form:**

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

**Describe the following set in the Roster Form:**

{x/x = 2n, n ∈ N}

**Describe the following set in the Set-Builder form:**

{0}

**Describe the following set in the Set-Builder form:**

{0, ±1, ±2, ±3}

**Describe the following set in the Set-Builder form:**

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

If A = {x/6x^{2} + x - 15 = 0}

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

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

find (A ∪ B ∪ C)

If A = {x/6x^{2} + x - 15 = 0}

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

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

find (A ∩ B ∩ C)

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)

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)

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)

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')

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'

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')

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)

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)

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)

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)

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)

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')

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.

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.

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

- at least one of the newspapers.
- neither Marathi nor English newspaper.
- Only one of the newspapers.

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.

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.

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Express {(x, y) / x^{2} +y^{2} = 100 where x, y ∈ W} as a set of ordered pairs.

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

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

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

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.

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

R_{1} = {(a, a^{2}) / a is prime number less than 15}

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

R_{2} = `{("a", 1/"a") "/" 0 < "a" ≤ 5, "a" ∈ "N"}`

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

Find the following relation as sets of ordered pairs:

{(x, y) / y = 3x, x ∈ {1, 2, 3}, y ∈ {3, 6, 9, 12}}

Find the following relation as sets of ordered pairs:

{(x, y) / y > x + 1, x ∈ {1, 2} and y ∈ {2, 4, 6}}

Find the following relation as sets of ordered pairs:

{(x, y) / x + y = 3, x, y ∈ {0, 1, 2, 3}}

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

**Write the following set in the set-builder form: **

{10, 20, 30, 40, 50}

**Write the following set in the set-builder form: **

{a, e, i, o, u)

**Write the following set in the set-builder form:**

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

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.

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.

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

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

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.

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).

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?

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?

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).

If A = {– 1, 1}, find A × A × A.

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

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

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

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

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

## Solutions for Chapter 1: Sets and Relations

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

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Concepts covered in Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board chapter 1 Sets and Relations are Introduction of Set, Relations of Sets, Types of Relations, Representation of a Set, Intervals, Types of Sets, Operations on Sets.

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