Question 1

Question 1: Write the following sets in set builder form: (i) {10, 20, 30, 40, 50} (ii) {a, e, i, o, u} (iii) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

Accepted Answer

(i) Let A = {10, 20, 30, 40, 50} ∴ A = {x / x = 10n, n ∈ N and n ≤ 5}

Question 2

Question 2: 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 sets (i) A ∪ B (ii) B ∩ C (iii) A – B (iv) B – C (v) A ∪ B ∪ C (vi) A ∩ (B

Accepted Answer

U = {x / x ∈ N, 1 ≤ x ≤ 12} = {1, 2, 3, …., 12} A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} (i) A ∪ B = {1, 2, 4, 6, 7, 10, 11}

Question 3

Question 3: 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 a

Accepted Answer

Let A = set of students who drink apple juice B = set of students who drink orange juice X = set of all students ∴ n(X) = 425, n(A) = 115, n(B) = 160, n(A ∩ B) = 80 No. of students who neither drink apple juice nor orange juice n(A’ ∩ B’) = n(A ∪ B)’ = n(X) – n(A ∪ B) = 425 – [n(A) + n(B) – n(A ∩ B)

Question 4

Question 4: 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?

Accepted Answer

Let A = set of teachers who teach Mathematics B = set of teachers who teach Physics n(A ∪ B) = 20, n(A) = 12, n(A ∩ B) = 4 Since, n(A ∪ B) = n(A) + n(B) – n(A ∩ B) ∴ 20 = 12 + n(B) – 4 ∴ n(B) = 12 ∴ Number of teachers who teach physics = 12

Question 5

Question 5: (i) 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). (ii) If A = {-1, 1}, find A × A × A.

Accepted Answer

(i) A = {1, 2, 3} and B = {2, 4} A × A = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)} A × B = {(1, 2), (1, 4), (2, 2), (2, 4), (3, 2), (3, 4)} B × A = {(2, 1), (2, 2), (2, 3), (4, 1), (4, 2), (4, 3)} B × B = {(2, 2), (2, 4), (4, 2), (4, 4)} (A × B) ∩ (B × A) = {(2, 2)}

Question 6

Question 6: If A = {1, 2, 3}, B = {4, 5, 6}, which of the following are relations from A to B. (i) R1 = {(1, 4), (1, 5), (1, 6)} (ii) R2 = {(1, 5), (2, 4), (3, 6)} (iii) R3 = {(1, 4), (1, 5),

Accepted Answer

A = {1, 2, 3}, B = {4, 5, 6} ∴ A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)} (i) R1 = {(1, 4), (1, 5), (1, 6)} Since, R1 ⊆ A × B ∴ R1 is a relation from A to B.

Question 7

Question 7: Determine the domain and range of the following relation. R = {(a, b) / a ∈ N, a < 5, b = 4}

Accepted Answer

R = {(a, b) / a ∈ N, a < 5, b = 4} ∴ Domain (R) = {a / a ∈ N, a < 5} = {1, 2, 3, 4} Range (R) = {b / b = 4} = {4}

Chapter 1 Sets and Relations Miscellaneous Exercise 1 Solutions