 A directory of Objective Type Questions covering all the Computer Science subjects. Here you can access and discuss Multiple choice questions and answers for various compitative exams and interviews.

 31. 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

 32. Consider the following statements: S1: There exists infinite sets A, B, C such that A ∩ (B ∪ C) is finite. S2: There exists two irrational numbers x and y such that (x+y) is rational. Which of the following is true about S1 and S2? a. Only S1 is correct b. Only S2 is correct c. Both S1 and S2 are correct d. None of S1 and S2 is correct

 33. A relation R is defined on the set of integers as xRy if f(x + y) is even. Which of the following statement is true? a. R is not an equivalence relation b. R is an equivalence relation having 1 equivalence class c. R is an equivalence relation having 2 equivalence classes d. R is an equivalence relation having 3 equivalence classes

 34. Let R be the relation on the set of positive integers such that aRb if and only if a and b are distinct and have a common divisor other than 1. Which one of the following statements about R is True? a. R is symmetric and reflexive but not transitive b. R is reflexive but not symmetric and not transitive c. R is transitive but not reflexive and not symmetric d. R is symmetric but not reflexive and not transitive

 35. The cardinality of the power set of {0, 1, 2 . . ., 10} is _________. a. 1024 b. 1023 c. 2048 d. 2043

 36. Consider two relations R1(A, B) with the tuples (1, 5), (3, 7) and R1(A, C) = (1, 7), (4, 9). Assume that R(A,B,C) is the full natural outer join of R1 and R2. Consider the following tuples of the form (A,B,C) a = (1, 5, null), b = (1, null, 7), c = (3, null, 9), d = (4, 7, null), e = (1, 5, 7), f = (3, 7, null), g = (4, null, 9). Which one of the following statements is correct? a. R contains a, b, e, f, g but not c, d b. R contains a, b, c, d, e, f, g c. R contains e, f, g but not a, b d. R contains e but not f, g

 37. The number of onto functions (surjective functions) from set X = {1, 2, 3, 4} to set Y = {a, b, c} is ________________ a. 36 b. 64 c. 81 d. 72