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61. A Relation R is defined on the set of integers as xRy if (x + y) is even. Which of the following statements is TRUE?
R is not an equivalence relation
R is an equivalence relation having one equivalence class
R is an equivalence relation having two equivalence classes
R is an equivalence relation having three equivalence classes
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62. Let P(S) denote the power set of set S. Which of the following is always TRUE ?
P(P(S)) = P(S)
P(S) ∩ S = P (S)
P(S) ∩ P(P(S)) = [ φ ]
S ∉ P(S)
63. If R be a symmetric and transitive relation on a set A, then
R is reflexive and hence an equivalence relation
R is reflexive and hence a partial order
R is not reflexive and hence not an equivalence relation
None of these
64. The number of binary relations on a set with n elements is
n2
2n^2
2n
65. If A and B be sets and Ac and Bc denote the complements of the sets A and B, then set (A — B) ∪ (B — A) ∪ (A ∩ B) is equal to
If A and B be sets and Ac and Bc denote the complements of the sets A and B, then set (A — B) ∪ (B — A) ∪ (A ∩ B) is equal to
A ∪ B
Ac ∪ Bc
A ∩ B
Ac ∩ Bc
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