1. If in sets A, B, C, the set B ∩ C consists of 8 elements, set A ∩ B consists of 7 elements and set C ∩ A consists of 7 elements then the minimum element in set A U B U C will be?
Correct : A. 8
2. Let (A7, ⊗7)=({1, 2, 3, 4, 5, 6}, ⊗7) is a
group. It has two sub groups X and Y. X={1, 3, 6}, Y={2, 3, 5}. What is the order of union of subgroups?
Correct : B. 5
3. A relation (34 × 78) × 57 = 57 × (78 × 34)
can have property.
Correct : B. associative
4. B1: ({0, 1, 2….(n-1)}, xm) where xn stands
for “multiplication-modulo-n” and B2: ({0, 1, 2….n}, xn) where xn stands for “multiplication-modulo-m” are the two statements. Both B1 and B2 are considered to be
Correct : B. semigroups
5. If group G has 65 elements and it has two subgroups namely K and L with order 14 and
30. What can be order of K intersection L?
Correct : C. 5
6. Consider the binary operations on X, a*b = a+b+4, for a, b ∈ X. It satisfies the properties of
Correct : A. abelian group
7. Let * be the binary operation on the rational number given by a*b=a+b+ab. Which of the following property does not exist for the group?
Correct : B. identity property
8. A group G, ({0}, +) under addition operation satisfies which of the following properties?
Correct : B. closure, associativity, inverse and identity
9. If (M, *) is a cyclic group of order 73, then number of generator of G is equal to
Correct : C. 72
10. The set of even natural numbers, {6, 8, 10, 12,..,} is closed under addition operation. Which of the following properties will it satisfy?
Correct : A. closure property
11. A non empty set A is termed as an algebraic structure
Correct : A. with respect to binary operation *
12. An algebraic structure is called a semigroup.
Correct : A. (p, *)
13. Condition for monoid is
Correct : D. (a*e)=(e*a)=a
14. A monoid is called a group if
Correct : D. (a*c)=(c*a)=e
15. Matrix multiplication is a/an
property.
Correct : B. associative
16. How many properties can be held by a group?
Correct : C. 5
17. A cyclic group is always
Correct : A. abelian group
18. {1, i, -i, -1} is
Correct : C. a trivial group
19. Let K be a group with 8 elements. Let H be a subgroup of K and H<K. It is known that the size of H is at least 3. The size of H is
Correct : C. cyclic group
20. is not necessarily a property of a Group.
Correct : A. commutativity
21. A group of rational numbers is an example of
Correct : B. a subgroup of a group of real numbers
22. Intersection of subgroups is a
Correct : B. subgroup
23. What is a circle group?
Correct : A. a subgroup complex numbers having magnitude 1 of the group of nonzero complex elements
24. A normal subgroup is
Correct : D. an invariant equipped with conjugation by the elements of original group
25. Two groups are isomorphic if and only if
is existed between them.
Correct : C. isomorphism
26. a * H is a set of coset.
Correct : B. left
27. a * H = H * a relation holds if
Correct : D. h is subgroup of an abelian group
28. Lagrange’s theorem specifies
Correct : B. the order of the subgroup divides the order of the finite group
29. A function is defined by f(x)=2x and f(x +
y) = f(x) + f(y) is called
Correct : A. isomorphic
30. An isomorphism of a group onto itself is called
Correct : D. automorphism
31. The elements of a vector space form a/an
under vector addition.
Correct : A. abelian group
32. A set of representatives of all the cosets is called
Correct : D. transversal
33. Which of the following statement is true?
Correct : C. the set of all non-singular matrices forms a group under multiplication
34. How many different non-isomorphic Abelian groups of order 8 are there?
Correct : C. 2
35. Consider the set B* of all strings over the alphabet set B = {0, 1} with the concatenation operator for strings
Correct : A. does not form a group
36. All groups satisfy properties
Correct : B. g-i to g-iv
37. An Abelian Group satisfies the properties
Correct : A. g-i to g-v
38. A Ring satisfies the properties
Correct : D. g-i to r-iii
39. A Ring is said to be commutative if it also satisfies the property
Correct : D. r-iv
40. An ‘Integral Domain’ satisfies the properties
Correct : C. g-i to r-vi
41. a.(b.c) = (a.b).c is the representation for which property?
Correct : A. g-ii
42. a(b+c) = ac+bc is the representation for which property?
Correct : D. r-iii
43. For the group Sn of all permutations of n distinct symbols, what is the number of elements in Sn?
Correct : D. n!
44. Does the set of residue classes (mod 3) form a group with respect to modular addition?
Correct : A. yes
45. Does the set of residue classes (mod 3) form a group with respect to modular addition?
Correct : B. no
46. The less-than relation, <, on a set of real numbers is
Correct : A. not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric
47. If the longest chain in a partial order is of length l, then the partial order can be written as disjoint antichains.
Correct : C. l
48. Suppose X = {a, b, c, d} and π1 is the partition of X, π1 = {{a, b, c}, d}. The number of ordered pairs of the equivalence relations induced by
Correct : B. 10
49. The inclusion of sets into R = {{1, 2}, {1, 2, 3}, {1, 3, 5}, {1, 2, 4}, {1, 2, 3, 4, 5}} is necessary and sufficient to make R a complete lattice under the partial order defined by set containment.
Correct : C. {1}
50. Consider the set N* of finite sequences of natural numbers with a denoting that sequence a is a prefix of sequence b. Then, which of the following is true?
Correct : A. every non-empty subset of has a greatest lower bound
51. A partial order ≤ is defined on the set S =
{x, b1, b2, … bn, y} as x ≤ bi for all i and bi ≤ y for all i, where n ≥ 1. The number of total orders on the set S which contain the partial order ≤ is
Correct : C. n!
52. A Poset in which every pair of elements has both a least upper bound and a greatest lower bound is termed as
Correct : B. lattice
53. If every two elements of a poset are comparable then the poset is called
Correct : B. totally ordered poset
54. A has a greatest element and a least element which satisfy 0<=a<=1 for every a in the lattice(say, L).
Correct : D. bounded lattice
55. The graph given below is an example of
Correct : A. non-lattice poset
56. A sublattice(say, S) of a lattice(say, L) is a convex sublattice of L if
Correct : C. x<=y<=z, where x, y in s implies z in s, for every element x, y, z in l
57. The graph is the smallest non-modular lattice N5. A lattice is if and only if it does not have a isomorphic to N5.
Correct : D. modular, sublattice
58. Every poset that is a complete semilattice must always be a
Correct : B. complete lattice
59. A free semilattice has the
property.
Correct : D. universal
60. Algebra of logic is termed as
Correct : C. arithmetic logic
61. What is the definition of Boolean functions?
Correct : B. a special mathematical function with n degrees such that f:yn–>y
62. F(X,Y,Z,M) = X`Y`Z`M`. The degree of the function is
Correct : C. 4
63. Which of the following is a Simplification law?
Correct : A. m.(~m+n) = m.n
64. What are the canonical forms of Boolean Expressions?
Correct : D. som and pom
65. Which of the following is/are the universal logic gates?
Correct : C. nand and nor
66. The logic gate that provides high output for same inputs
Correct : B. x-nor
67. The of all the variables in direct or complemented from is a maxterm.
Correct : A. addition
68. What is the use of Boolean identities?
Correct : A. minimizing the boolean expression
69. Inversion of single bit input to a single bit output using
Correct : A. not gate
70. There are numbers of Boolean functions of degree n.
Correct : B. 2(2*n)
71. A is a Boolean variable.
Correct : A. literal
72. Minimization of function F(A,B,C) = A*B*(B+C) is
Correct : D. ab
73. The set for which the Boolean function is functionally complete is
Correct : B. {., +, -}
74. (X+Y`)(X+Z) can be represented by
Correct : A. (x+y`z)
75. is a disjunctive normal form.
Correct : C. sum-of-products
76. a ⊕ b =
Correct : A. (a+b)(a`+b`)
77. Find the simplified expression A’BC’+AC’.
Correct : C. (a+b)c’
78. Evaluate the expression: (X + Z)(X + XZ’)
+ XY + Y.
80. What is the simplification value of MN(M
+ N’) + M(N + N’)?
Correct : B. mn+m’n’ c) (1+m)
81. Simplify the expression XZ’ + (Y + Y’Z) + XY.
TOPIC 5.5 MINIMIZATION OF BOOLEAN ALGEBRA
Correct : C. (x + y +z)
82. Find the simplified term Y’ (X’ + Y’) (X + X’Y)?
Correct : A. xy’
83. If an expression is given that x+x’y’z=x+y’z, find the minimal expression of the function F(x,y,z) = x+x’y’z+yz?
Correct : C. x + z
84. Simplify the expression: XY’ + X’ + Y’X’.
Correct : C. (xy)’
85. Minimize the Boolean expression using Boolean identities: A′B+ABC′+BC’+AB′C′.
Correct : A. b(ac)’ + ac’
86. Minimize the following Boolean expression using Boolean identities. F(A,B,C) = (A+BC’)(AB’+C)
Correct : D. a(b’ + c)
87. Which of the following statement is a proposition?
Correct : D. The only odd prime number is 2
88. The truth value of ‘4+3=7 or 5 is not prime’.
Correct : B. True
89. Which of the following option is true?
Correct : A. If the Sun is a planet, elephants will fly
90. What is the value of x after this statement, assuming the initial value of x is 5?
‘If x equals to one then x=x+2 else x=0’.
Correct : C. 0
91. Let P: I am in Bangalore.; Q: I love cricket.; then q -> p(q implies p) is?
Correct : A. If I love cricket then I am in Bangalore
92. Let P: If Sahil bowls, Saurabh hits a century.; Q: If Raju bowls, Sahil gets out on first ball. Now if P is
true and Q is false then which of the following can be true?
Correct : C. Sahil bowled and Saurabh hits a century
93. The truth value ‘9 is prime then 3 is even’.
Correct : B. TTru
94. Let P: We should be honest., Q: We should be dedicated., R: We should be overconfident. Then ‘We
should be honest or dedicated but not overconfident.’ Is best represented by?
Correct : D. P V Q ∧ ~R
95. If there are n distinct components in a statement then there are _______ combinations of
values in the truth table.
Correct : A. 2^n
96. If P then Q is called _________ statement
Correct : C. conditional
97. (P->Q)-> (^Q) is __________.
Correct : A. not a well formed formula
98. A relation R in a set X is symmetric if ________.
Correct : C. xRy=>yRx
99. If a relation is reflexive, then all the diagonal entries in the relation matrix must be________.
Correct : B. 1
100. If R is reflexive, symmetric and transitive then the relation is said to be ________.