 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.

 21. Let f: B → C and g: A → B be two functions and let h = f o g. Given that h is an onto function. Which one of the following is TRUE? a. f and g should both be onto functions b. f should be onto but g need not be onto c. g should be onto but f need not be onto d. both f and g need not be onto

 22. What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs (a, b) and (c, d) in the chosen set such that "a ≡ c mod 3" and "b ≡ d mod 5" . a. 4 b. 6 c. 16 d. 24

 23. Consider the binary relation:S = {(x, y) | y = x+1 and x, y ∈ {0, 1, 2, ...}}The reflexive transitive closure of S is a. {(x, y) | y > x and x, y ∈ {0, 1, 2, ... }} b. {(x, y) | y ≥ x and x, y ∈ {0, 1, 2, ... }} c. {(x, y) | y < x and x, y ∈ {0, 1, 2, ... }} d. {(x, y) | y ≤ x and x, y ∈ {0, 1, 2, ... }}

 24. The following is the incomplete operation table a 4-element group. *  e  a  b  c e  e  a  b  c a  a  b  c  e b  c The last row of the table is a. c a e b b. c b a e c. c b e a d. c e a b

 25. The inclusion of which of the following sets intoS = {{1, 2}, {1, 2, 3}, {1, 3, 5}, (1, 2, 4), (1, 2, 3, 4, 5}}is necessary and sufficient to make S a complete lattice under the partial order defined by set containment ? a. {1} b. {1}, {2, 3} c. {1}, {1, 3} d. {1}, {1, 3}, (1, 2, 3, 4}, {1, 2, 3, 5)

 26. Consider the set ∑* of all strings over the alphabet ∑ = {0, 1}. ∑* with the concatenation operator for strings a. does not form a group b. forms a non-commutative group c. does not have a right identity element d. forms a group if the empty string is removed from ∑*

 27. Let (5, ≤) be a partial order with two minimal elements a and b, and a maximum element c.Let P : S → {True, False} be a predicate defined on S.Suppose that P(a) = True, P(b) = False and P(x) ⇒ P(y) for all x, y ∈ S satisfying x ≤ y, where ⇒ stands for logical implication.Which of the following statements CANNOT be true ? a. P(x) = True for all x ∈ S such that x ≠ b b. P(x) = False for all x ∈ S such that x ≠ a and x ≠ c c. P(x) = False for all x ∈ S such that b ≤ x and x ≠ c d. P(x) = False for all x ∈ S such that a ≤ x and b ≤ x