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
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Answer: (c).h is onto => g is 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!
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Answer: (b).n + 1

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 reflexive
Q: R is transitive

Which 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
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Answer: (b).P is true and Q is 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 - 3
2. 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
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Answer: (a).I and II only

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)
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Answer: (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
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Answer: (b).satisfiable and so is its negation

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
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Answer: (c).Neither I nor II

48. What is the cardinality of the set of integers X defined below? X = {n | 1 ≤ n ≤ 123, n is not divisible by either 2, 3 or 5} ?
a. 28
b. 33
c. 37
d. 44
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Answer: (b).33

49. Let A = {a, b, c, d }, B = { p, q, r, s } denote sets. R : A –> B, R is a function from A to B. Then which of the following relations are not functions ?

(i) { (a, p) (b, q) (c, r) }
(ii) { (a, p) (b, q) (c, s) (d, r) }
(iii) { (a, p) (b, s) (b, r) (c, q) }
a. (i) and (ii) only
b. (ii) and (iii) only
c. (i) and (iii) only
d. None of these
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Answer: (c).(i) and (iii) only

50. Let A = { 1,2,3,4,…….∞ } and a binary operation ‘+’ is defined by a + b = ab ∀ a,b ∈ A. Which of the following is true ?
a. ( A, + ) is a semi group but not monoid
b. ( A, + ) is a monoid but not group
c. ( A, + ) is a group
d. ( A, + ) is not a semi group
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Answer: (b).( A, + ) is a monoid but not group

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