Q. 2 Consider the following relations:
R1(a,b) iff (a+b) is even over the set of integers R2(a,b) iff (a+b) is odd over the set of integers R3(a,b) iff a.b > 0 over the set of non-zero rational numbers R4(a,b) iff |a - b| <= 2 over the set of natural numbers
Which of the following statements is correct?
(A) R1 and R2 are equivalence relations, R3 and R4 are not
(B) R1 and R3 are equivalence relations, R2 and R4 are not
(C) R1 and R4 are equivalence relations, R2 and R3 are not
(D) R1, R2, R3 and R4 are all equivalence relations
Answer: (B)
Explanation:
