Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board chapter 5 - Sets and Relations [Latest edition]

Describe the following set in Roster form

A = {x/x is a letter of the word 'MOVEMENT'}

Describe the following set in Roster form

B = `{x//x  "is an integer", -3/2 < x < 9/2}`

Describe the following set in Roster form

C = {x/x = 2n + 1, n ∈ N}

Describe the following set in Set-Builder form

{0}

Describe the following set in Set-Builder form

{0, ±1, ±2, ±3}

Describe the following set in Set-Builder form

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

Describe the following set in Set-Builder form

{0, –1, 2, –3, 4, –5, 6, ...}

If A = {x/6x² + x – 15 = 0}, B = {x/2x² – 5x – 3 = 0}, C = {x/2x² – x – 3 = 0} then find (A ∪ B ∪ C).

If A = {x/6x² + x – 15 = 0}, B = {x/2x² – 5x – 3 = 0}, C = {x/2x² – 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' respective, 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:

(A ∪ B) = (A − B) ∪ (A ∩ B) ∪ (B − A)

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:

n(A ∪ B) = n(A) + n(B) – n(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(B) = (A' ∩ 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')

In a class of 200 students who appeared in certain examinations, 35 students failed in CET, 40 in NEET and 40 in JEE, 20 failed in CET and NEET, 17 in NEET and JEE, 15 in CET and JEE, and 5 failed in all three examinations. Find how many students, did not fail in any examination.

In a class of 200 students who appeared in certain examinations, 35 students failed in CET, 40 in NEET and 40 in JEE, 20 failed in CET and NEET, 17 in NEET and JEE, 15 in CET and JEE, and 5 failed in all three examinations. Find how many students, failed in NEET or JEE 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

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 neither Marathi and English newspaper

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 Only one of the newspapers

In a hostel, 25 students take tea, 20 students take coffee, 15 students take milk, 10 students take bot 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 total number of students in the hostel.

There are 260 persons with skin disorders. If 150 had been exposed to chemical A, 74 to 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 chemical A, 74 to 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

Write down the power set of A = {1,2,3}

Write the following interval in Set-Builder form:

(– 3, 0)

Write the following interval in Set-Builder form:

[6, 12]

Write the following interval in Set-Builder form

`(6, ∞)`

Write the following interval in Set-Builder form

`(-∞, 5]`

Write the following interval in Set-Builder form

(2, 5]

Write the following interval in Set-Builder form

[– 3, 4)

A college awarded 38 medals in volleyball, 15 in football, and 20 in basketball. The medals awarded to a total of 58 players and only 3 players got medals in all three sports. How many received medals in exactly two of the three sports?

Solve the following inequality and write the solution set using interval notation

− 9 < 2x + 7 ≤ 19

Solve the following inequality and write the solution set using interval notation

x² − x > 20

Solve the following inequality and write the solution set using interval notation

`(2x)/(x - 4) ≤ 5`

Solve the following inequality and write the solution set using interval notation

6x² + 1 ≤ 5x

If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A ∪ B 

If A = (–7, 3], B = [2, 6] and C = [4, 9] then find B ∪ C

If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A ∪ C

If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A ∩ B

If A = (–7, 3], B = [2, 6] and C = [4, 9] then find B ∩ C

If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A ∩ C

If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A' ∩ B

If A = (–7, 3], B = [2, 6] and C = [4, 9] then find B' ∩ C'

If A = (–7, 3], B = [2, 6] and C = [4, 9] then find B – C

If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A – B

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

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

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

If P = {1, 2, 3) and Q = {1, 4}, find sets P × Q and Q × P

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

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

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

Let A = {6, 8} and B = {1, 3, 5}
Show that R₁ = {(a, b)/a ∈ A, b ∈ B, a − b is an even number} is a null relation. R₂ = {(a, b)/a ∈ A, b ∈ B, a + b is odd number} is an universal relation

Write the relation in the Roster Form. State its domain and range

R₁ = {(a, a²)/a is prime number less than 15}

Write the relation in the Roster Form. State its domain and range

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

Write the relation in the Roster Form. State its domain and range

R₃ = {(x, y)/y = 3x, y∈ {3, 6, 9, 12}, x∈ {1, 2, 3}

Write the relation in the Roster Form. State its domain and range

R₄ = {(x, y)/y > x + 1, x = 1, 2 and y = 2, 4, 6}

Write the relation in the Roster Form. State its domain and range

R₅ = {(x, y)/x + y = 3, x, y∈ {0, 1, 2, 3}

Write the relation in the Roster Form. State its domain and range

R₆ = {(a, b)/a ∈ N, a < 6 and b = 4}

Write the relation in the Roster Form. State its domain and range

R₇ = {(a, b)/a, b ∈ N, a + b = 6}

Write the relation in the Roster Form. State its domain and range

R₈ = {(a, b)/b = a + 2, a ∈ z, 0 < a < 5}

Identify which of if the following relations are reflexive, symmetric, and transitive.

For the set A = {a, b, c, d, e}, the correct statement is ______. 

Select the correct answer from given alternative.

If aN = {ax : x ∈ N}, then set 6N ∩ 8N =

Select the correct answer from given alternative.

If set A is empty set then n[P [P [P (A)]]] is

Select the correct answer from given alternative.

In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then, persons travelling by car or bus are

Select the correct answer from given alternative.

If the two sets A and B are having 43 elements in common, then the number of elements common to each of the sets A × B and B × A is

Select the correct answer from given alternative.

Let R be a relation on the set N be defined by {(x, y)/x, y ∈ N, 2x + y = 41} Then R is ______.

Select the correct answer from given alternative.

The relation ">" in the set of N (Natural number) is

Select the correct answer from given alternative.

A relation between A and B is

Select the correct answer from given alternative.

If (x, y) ∈ R × R, then xy = x² is a relation which is

Select the correct answer from given alternative

If A = {a, b, c} The total no. of distinct relations in A × A is

Answer the following:

Write down the following set in set-builder form

{10, 20, 30, 40, 50}

Answer the following:

Write down the following set in set-builder form

{a, e, i, o, u)

Answer the following:

Write down the following set in set-builder form

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

Answer the following:

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 down the set A ∪ B

Answer the following:

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 down the set B ∩ C

Answer the following:

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 down the set A – B

Answer the following:

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 down the set B ∩ C'

Answer the following:

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 down the set A ∪ B ∪ C

Answer the following:

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 down the set A ∩ (B ∪ C)

Answer the following:

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?

Answer the following:

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?

Answer the following:

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)

Answer the following:

If A = {−1, 1} , find A × A × A

Answer the following:

If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range

R₁ = {(1, 4), (1, 5), (1, 6)}

Answer the following:

If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range

R₂ = {(1, 5), (2, 4), (3, 6)}

Answer the following:

If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range

R₃ = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}

Answer the following:

If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range

R₄ = {(4, 2), (2, 6), (5, 1), (2, 4)}

Answer the following:

Determine the domain and range of the following relation.

R = {(a, b)/a ∈ N, a < 5, b = 4}

Answer the following:

Determine the domain and range of the following relation.

R = {(a, b)/b = |a – 1|, a ∈ Z, IaI < 3}

Answer the following:

Find R : A → A when A = {1, 2, 3, 4} such that R = (a, b)/a − b = 10}

Answer the following:

Find R : A → A when A = {1, 2, 3, 4} such that R = {(a, b)/|a − b| ≥ 0}

Answer the following:

R = {1, 2, 3} → {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} Check if R is reflexive

Answer the following:

R = {1, 2, 3} → {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} Check if R is symmentric

Answer the following:

R = {1, 2, 3} → {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} Check if R is transitive

Answer the following:

Check if R : Z → Z, R = {(a, b)/2 divides a – b} is equivalence relation.

Answer the following:

Show that the relation R in the set A = {1, 2, 3, 4, 5} Given by R = {(a, b)/|a − b| is even} is an equivalence relation.

Answer the following:

Show that the following is an equivalence relation

R in A is set of all books. given by R = {(x, y)/x and y have same number of pages}

Answer the following:

Show that the following is an equivalence relation

R in A = {x ∈ Z | 0 ≤ x ≤ 12} given by R = {(a, b)/|a − b| is a multiple of 4}

Answer the following:

Show that the following is an equivalence relation

R in A = {x ∈ N/x ≤ 10} given by R = {(a, b)/a = b}