## Sets and Functions

#### Sets and Functions

1. Let A = {x: x ∈ N ∧ x is a multiple of 2}
B = {x: x ∈ N ∧ x is a multiple of 5}
C = {x: x ∈ N ∧ x is a multiple of 10}
Describe the set A ∩ (B ∪ C)

1. B = {5, 10, 15,…}
C = {10, 20, 30,…}
∴ A ∩ (B ∩ C) = {2, 4, 6,…} ∩ {5, 10, 15,…}

##### Correct Option: C

B = {5, 10, 15,…}
C = {10, 20, 30,…}
B ∪ C = {5, 10, 15,…} ∪ {10, 20, 30,…}
B ∪ C = {5, 10, 15,…}
∴ A ∩ (B ∩ C) = {2, 4, 6,…} ∩ {5, 10, 15,…} = {10, 20, 20,…} = C.

1. If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩ T has 11 elements, how many elements does S ∪ T have?

1. Given in the question,
n(S) = 21, n(T) = 32, n(S ∩ T) = 11, n(S ∪ T) = ?
Using the formula,
n(S ∪ T) = n(S) + n(T) – n(S ∩ T)

##### Correct Option: C

Given in the question,
n(S) = 21, n(T) = 32, n(S ∩ T) = 11, n(S ∪ T) = ?
Using the formula,
n(S ∪ T) = n(S) + n(T) – n(S ∩ T) = 21 + 32 – 11 = 42
Hence, S ∪ T has 42 elements.

1. If U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, A = {3, 5, 7, 9, 11} and B = {7, 8, 9, 10, 11}, Then compute (A – B)′.

1. A – B is a set of member which belong to A but does not belongs to B

##### Correct Option: D

A – B is a set of member which belong to A but do not belong to B
∴ A – B = {3, 5, 7, 9, 11} - {7, 8, 9, 10, 11}
A – B = {3, 5}
According to formula,
(A − B)′ = U - (A – B)

∴ (A − B)′ = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11} - {3, 5}
(A − B)′ = {2, 4, 6, 7, 8, 9, 10, 11}.

1. Let A = {1, 2}, B = {2, 3}. Evaluate A × B.

1. A × B = {1, 2} × {2, 3}

##### Correct Option: C

A × B = {1, 2} × {2, 3}
= {(1, 2), (1, 3), (2, 2), (2, 3)}.

1. Which of the following statements is true?

1. NA

NA