Sets and Functions
 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)

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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.
 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?

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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.
 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)′.

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

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A × B = {1, 2} × {2, 3}
Correct Option: C
A × B = {1, 2} × {2, 3}
= {(1, 2), (1, 3), (2, 2), (2, 3)}.
 Which of the following statements is true?

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NA
Correct Option: A
NA