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
View Answer Report Discuss Too Difficult! Search Google
Answer: (b).f should be onto but 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
View Answer Report Discuss Too Difficult! Search Google
Answer: (c).16

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, ... }}
View Answer Report Discuss Too Difficult! Search Google
Answer: (b).{(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
View Answer Report Discuss Too Difficult! Search Google
Answer: (d).c e a b

25. The inclusion of which of the following sets into

S = {{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)
View Answer Report Discuss Too Difficult! Search Google
Answer: (a).{1}

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 ∑*
View Answer Report Discuss Too Difficult! Search Google
Answer: (a).does not form a group

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
View Answer Report Discuss Too Difficult! Search Google
Answer: (d).P(x) = False for all x ∈ S such that a ≤ x and b ≤ x

28. Let f : A → B be an injective (one-to-one) function.

Define g : 2^A → 2^B as :
g(C) = {f(x) | x ∈ C}, for all subsets C of A.
Define h : 2^B → 2^A as :
h(D) = {x | x ∈ A, f(x) ∈ D}, for all subsets D of B.

Which of the following statements is always true ?
a. g(h(D)) ⊆ D
b. g(h(D)) ⊇ D
c. g(h(D)) ∩ D = ф
d. g(h(D)) ∩ (B - D) ≠ ф
View Answer Report Discuss Too Difficult! Search Google
Answer: (a).g(h(D)) ⊆ D

29. Which of the following is true?
a. The set of all rational negative numbers forms a group under multiplication
b. The set of all non-singular matrices forms a group under multiplication
c. The set of all matrices forms a group under multiplication
d. Both (2) and (3) are true
View Answer Report Discuss Too Difficult! Search Google
Answer: (b).The set of all non-singular matrices forms a group under multiplication

30. The binary relation S = ф (empty set) on set A = {1, 2, 3} is :
a. Neither reflexive nor symmetric
b. Symmetric and reflexive
c. Transitive and reflexive
d. Transitive and symmetric
View Answer Report Discuss Too Difficult! Search Google
Answer: (d).Transitive and symmetric

Page 3 of 23