 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.

 41. Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a ∈ A. Which of the following statements is always true for all such functions f and g? a. g is onto => h is onto b. h is onto => f is onto c. h is onto => g is onto d. h is onto => f and g are onto

 42. Let A be a set with n elements. Let C be a collection of distinct subsets of A such that for any two subsets S1 and S2 in C, either S1 ⊂ S2 or S2⊂ S1. What is the maximum cardinality of C? a. n b. n + 1 c. 2n-1 + 1 d. n!

 43. A binary relation R on N x N is defined as follows:(a, b) R (c, d) if a <= c or b <= d.Consider the following propositions:P: R is reflexiveQ: R is transitiveWhich one of the following statements is TRUE? a. Both P and Q are true b. P is true and Q is false c. P is false and Q is true d. Both P and Q are false

 44. For the set N of natural numbers and a binary operation f : N x N → N, an element z ∊ N is called an identity for f, if f (a, z) = a = f(z, a), for all a ∊ N. Which of the following binary operations have an identity?1. f (x, y) = x + y - 32. f (x, y) = max(x, y)3. f (x, y) = x^y a. I and II only b. II and III only c. I and III only d. None of these

 45. Given a boolean function f (x1, x2, ..., xn), which of the following equations is NOT true a. f (x1, x2, ..., xn) = x1'f(x1, x2, ..., xn) + x1f(x1, x2, ..., xn) b. f (x1, x2, ..., xn) = x2f(x1, x2, …, xn) + x2'f(x1, x2, …,xn) c. f (x1, x2, ..., xn) = xn'f(x1, x2, …, 0) + xnf(x1, x2, …,1) d. f (x1, x2, ..., xn) = f(0, x2, …, xn) + f(1, x2, .., xn)

 46. Consider the following first order logic formula in which R is a binary relation symbol. ∀x∀y (R(x, y)  => R(y, x)) The formula is a. satisfiable and valid b. satisfiable and so is its negation c. unsatisfiable but its negation is valid d. satisfiable but its negation is unsatisfiable

 47. Let P, Q and R be sets let Δ denote the symmetric difference operator defined as PΔQ = (P U Q) - (P ∩ Q). Using Venn diagrams, determine which of the following is/are TRUE? PΔ (Q ∩ R) = (P Δ Q) ∩ (P Δ R) P ∩ (Q ∩ R) = (P ∩ Q) Δ (P Δ R) a. I only b. II only c. Neither I nor II d. Both I and II