1 - "n/m" means that n is a factor of m, then the relation T is
relexive, transitive and not symmetric
2 - (A ∪ B) ∪ C =
A ∪ ( B ∪ C)
3 - (A’)’ = ?
A
4 - { (a, b) : a² +b² = 1} on the set S has the following relation
symmetric
5 - A — B will contain elements in ?
A not in B
6 - A = {x: x ≠ x }represents
{}
7 - A C B is read as ?
A is a proper subset of B
8 - A compound statement of form " if p then q " is called an
implication
9 - A conditional statemnt is regarded as false only antecedent is true and consequent is
FALSE
10 - A conjunction of two statement p and q is true only if
both p and q are true
11 - A declarative statement which may be true or false but not both is called
Proposition
12 - A partition of {1, 2, 3, 4, 5} is the family
{(1, 2,), (3, 4, 5)}
13 - A Relation R is defined on the set of integers as xRy if (x + y) is even. Which of the following statements is TRUE?
R is an equivalence relation having two equivalence classes
14 - A set consisting of a definite number of elements is called a
Finite set
15 - A set contains k elements. The power set of this set contains
2k elements
16 - A set has n elements, then the, number of elements in its power set is ?
m x n
17 - A set is known by its _______.
Elements
18 - A subset of A x A is called a
Relation in A
19 - A subset of B x A is called a
Relation from B to A
20 - A Subset of B x B is called a
Relation in B
21 - A survey showed that 63 % of the Americans like cheese whereas 76 % like apples. If x % of Americans like both cheese and apples, then find the range of x?
0 ≤ x ≤ 39 %
22 - A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples, then we have
39 ? x ? 63
23 - A’ will contain how many elements from the original set A
0
24 - A—B is read as ?
Difference of A and B of B and A
25 - An implication or conditional "if p then q "is denoted by
p → q
26 - Conjunction of two statement p and q is denoted by
p Ʌ q
27 - Disjunction of two statements p and q is denoted by
p ˅ q
28 - Empty set is a ?
Finite Set
29 - Every set is a ___________ of itself
Improper subset
30 - G(e, a, b, c} is an abelian group with 'e' as identity element. The order of the other elements are
2,2,3
31 - How many rational and irrational numbers are possible between 0 and 1 ?
Infinite
32 - Identity relation in A = {1,2,3,4,5,6} is
{(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}
33 - If (G, .) is a group such that (ab)- 1 = b-1 a-1, ∀ a, b ∈ G, then G is a/an
abelian group
34 - If (G, .) is a group such that a2 = e, ∀ a ∈ G, then G is
abelian group
35 - If * is defined on R* as a * b = (ab/2) then identity element in the group (R*, *) is
2
36 - If A = (1, 2, 3, 4). Let ~ = ((1, 2), (1, 3), (4, 2). Then ~ is
transitive
37 - If A = {(x, y) : x2 + y2 = 1; x, y ? R} and B = {(x, y): x2 + y2 = 4; x, y ?R} then
A ? B = ?
38 - If A = {0,2) and B = {1,3), then Cartesian product ?
AxB not equal BxA
39 - If A = {1, 2, 3, 4, 5}, then the number of proper subsets of A is
31
40 - If A = {1, 2, 3, 6, 11,18, 21}, B = {5, 7, 9} and N is the universal set, then A’ U ((AU B) ? B’) is equal to
N
41 - If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is
both symmetric and anti-symmetric
42 - If A = {1, 2, 5} and B = {3, 4, 5, 9}, then A ? B is equal to
{1, 2, 3, 4, 9}
43 - If A = {1, 2, 5} and B = {3, 4, 5, 9}, then A ? B is equal to If A = {x: x = 3n, n ? 6, n ? N} and B = {x: x = 9n, n ? 4, n ? N}, then which of the following is false?
A ? B = {9, 81, 729, 6561}
44 - If A = {4n -3n -1: n ? N} and B = {9(n-1): n ? N}, then we have
A Ì B
45 - If A = {x ? C: x2 = 1} and B = {x ? C: x4 = 1}, then A ? B is equal to
{-i, i}
46 - If A =[5,6,7] and B=[7,8,9]then A U B is equal to:
[5,6,7,8,9]
47 - If A ∩ B = B, then.
A ⊂ B
48 - If A and B are any two sets, then A ∩ (A ∪ B) is equal to
A
49 - If A and B are any two sets, then A ∪ (A ∩ B) is equal to.
A
50 - If A and B are sets and A∪ B= A ∩ B, then
A = B
51 - If A and B are two sets containing respectively m and n distinct elements. How many different relations can be defined for A and B?
2mn
52 - If A Í B then which of the following are correct?
All of these
53 - If A Í B, then B’ – A’ is equal to
?
54 - If A is any set, then
A ∩ A' = U
55 - If A is not equal to B, then the Cartesian product ?
A x B not equal B x A
56 - If A U B = AU C and A ? B = A ? C, then
B = C
57 - If A, B and C are any three sets, then A – (B ∪ C) is equal to
(A - B) ∩ (A - C)
58 - If A, B and C are any three sets, then A × (B ∪ C) is equal to.
(A × B) ∪ (A × C)
59 - If A, B, C be three sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C, then.
B = C
60 - If aN = {an : n ? N} and bN ? cN = dN, where a, b, c ? N and b, c are coprime, then
d = bc
61 - If every element of a group G is its own inverse, then G is
abeian
62 - If f : A ---> B is a bijective function, then f -1 of f =
IA(Identity map of the set A)
63 - If f : R ---->R defined by f(x) = x2 + 1, then values of f -1 (17) and f -1(-3) are respectively
{4,-4},Ø
64 - If f : X -> Y and a, b ⊆ X, then f (a ∩ b) is equal to
a proper subset of f(a) ∩ f(b)
65 - If f(x) = Log [(1 + x)/(1-x), then f (2x )/(1 + x²) is equal to
2 f (x)
66 - If for a ? N, aN = {ax: x ? N}, then the set 6 N ? 8 N is equal to
48N
67 - If for two sets A and B, A U B = A? B = A, then we have
A = B
68 - If n (A) = 115, n (B) = 326, n (A-B) = 47, then n (A U B) is equal to
373
69 - If R = ((1, 1), (3, 1), (2, 3), (4, 2)), then which of the following represents R2, where R2 is R composite R?
((1, 1), (2, 1), (4, 3), (3, 1))
70 - If R = {(1, 2),(2, 3),(3, 3)} be a relation defined on A= {1, 2, 3} then R . R( = R2) is
{(1, 3),(2, 3),(3, 3)}
71 - If R = {(1,1),(2,3),(4,5)}, then domain of the function is ?
Range R = {I,3,5}
72 - If R = {(1,1),(2,3),(4,5)}, then domain of the function is ?
Dom R {1,3,5}
73 - If R be a symmetric and transitvie relation on a set A, then
None of these
74 - If R is a relation on a finite set having a elements , then the number of relations on A is
2a2
75 - If R is a relation on a finite set having a elements , then the number of relations on A is
2a²
76 - If R is the relation “is greater than” from A ={1,2,3,4,5}to B={1,3,4} , Than R-1 is
{(1,2), (1,3), (1,4), (3,4), (1,5), (3,5), (4,5)}
77 - If the binary operation * is deined on a set of ordered pairs of real numbers as (a, b) * (c, d) = (ad + bc, bd) and is associative, then (1, 2) * (3, 5) * (3, 4) equals
(74,40)
78 - If the set has p elements, b has q elements, the no of elements in A x B is
pq
79 - If X = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {x ? N: 30 < x2 < 70}, B = {x : x is a prime number less than 10}, then which of the following is false:
A? B = {7, 8}
80 - If x ≠ 1, and f(x) = x + 1 / x – 1 is a real function, then f(f(f(2))) is
3
81 - If X and Y are two sets, then X ∩ (Y ∪ X) C equals
Ø
82 - If Y is the smallest set such that Y U {1, 2} = {1, 2, 3, 5, 9}, then Y is equal to
{3,5,9}
83 - In 2nd quadrant ?
X < 0, Y > 0
84 - In 3rd quadrant ?
X < 0, Y > 0
85 - In 4th quadrant ?
X > 0, Y < 0
86 - In a beauty contest, half the number of experts voted for Mr. A and two thirds voted for Mr. B. 10 voted for both and 6 did not vote for either. How many experts were there in all ?
24
87 - In a set – builder method, the null set is represented by
{ x : x ≠ x}
88 - In a statement "if p then q" q is
conclusion
89 - In lst quadrant ?
X > 0, Y > 0
90 - Let A = {0, 1} × {0, 1} × {0, 1} and B = {a, b, c} × {a, b, c} × {a, b, c}. Suppose A is listed in lexicographic order based on 0 < 1 and B is listed in lexicographic order based on a < b < c. If A×B
((1, 0, 0),(a, a, a),(0, 0, 0))
91 - Let A = {0, 1} × {0, 1} and B = {a, b, c}. Suppose A is listed in lexicographic order based on 0 < 1 and B is in alphabetic order. If A × B × A is listed in lexicographic order, then the next element
((1, 1), a,(0, 0))
92 - Let A = {1, 2, .....3 } Define ~ by x ~ y ⇔ x divides y. Then ~ is
a partial-ordering relation
93 - Let A = {x: x is a digit in the number 3591}, B = {x: x ? N, x<10}. Which of the following is false?
A-B = {2,4,6,7,8}
94 - Let f : R → R be defined by f(x)= {x+2 (x ≤ -1) { x2 (-1 ≤ x ≤1) {2 - x (x ≥ 1) Then value of f (-1.75) + f (0.5) + f (1.5) is
1
95 - Let f : X → Y . Consider the statement, “For all subsets C and D of Y , f −1 (C∩Dc ) = f −1 (C) ∩ [f −1 (D)]c . This statement is
True and equivalent to:For all subsets C and D of Y , f −1 (C − D) = f −1 (C) − f −1 (D).
96 - Let f : X → Y and g : Y → Z. Let h = g ◦ f : X → Z. Suppose g is one-to-one and onto. Which of the following is FALSE?
If f is one-to-one then h is one-to-one and onto
97 - Let f = {(x, x² /1+x² ): x € R } be a function from R into R . range of x is
any positive real number x such that 0≤ x <1
98 - Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered pairs (a, b) are there with a ∈ A and b ∈ B ?
p x q
99 - Let P(S) denote the power set of set S. Which of the following is always TRUE ?
P(S) ∩ P(P(S)) = [ φ ]
100 - Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B = Ø Then (pick the TRUE statement)
R is symmetric and not transitive
101 - Let R be a relation "(x -y) is divisible by m", where x, y, m are integers and m > 1, then R is
equivalence relation
102 - Let R be a relation N define by x + 2y = 8 . The domain of R is
{2,4,6}
103 - Let R be na equivalence relation on the set {1,2,3,4,5,6} given by {(1,1),(1,5),(2,2),(2,3),(2,6),(3,2),(3,3),(3,6),(4,4),(5,1),(5,5),(6,2),(6,6),(6,6)}. The partition included by R is
{{1,5},{2,3,6},{4}}
104 - Let R= {(x,y) :x, y belong to N, 2x+y =41}. The range is of the relation R is
{(2n-1) : n belongs to N, 1≤ n≤ 20}
105 - Let S be an infinite set and S1, S2, S3, ..., Sn be sets such that S1 ∪S2 ∪S3∪ .......Sn = S then
atleast one of the sets Si is an ininite set
106 - Let X be the universal set for sets A and B. If n (A) = 200, n (B) = 300 and n (A?B) = 100, then n(A’? B’) is equal to 300 provided n(X) is equal to
700
107 - Let Z denote the set of all integers. Define f : Z —> Z by f(x) = {x / 2 (x is even) 0 (x is odd) then f is
onto but not one-one
108 - Let σ = 452631 be a permutation on {1, 2, 3, 4, 5, 6} in one-line notation (based on the usual order on integers). Which of the following is NOT a correct cycle notation for σ?
(461)(352)
109 - Number of subsets of a set of 4 elements
16
110 - Number of subsets of a set of order three is
8
111 - P: 4 < 7, q: 6 > 11, conjuntion pɅ q is
FALSE
112 - P: 7 < 4, q: 6 > 11, disjuntion p˅q is
FALSE
113 - Set of first element of ordered pair forming a relation is called its
Range
114 - Set of rational numbers Q is a subset of
The set of Complex numbers.
115 - Set of real number R is a subset of
The set of Complex numbers
116 - Set of Second element of ordered pair forming a relation is called its
Domain
117 - Solve f(x) = √9-x² the range is
{x: 0≤ x ≤ 3}
118 - Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?
(g o h)²= g²o h² for every g,h ∈ G
119 - The binary relation S = Φ (empty set) on set A = {1, 2,3} is
transitive and symmetric
120 - The intersection of sets A and B is expressed as ?
AnB
121 - The number of elements in the power set of the set {{a, b}, c} is
4
122 - The number of elements in the Power set P(S) of the set S = [ [ Φ] , 1, [ 2, 3 ]] is
8
123 - The number of proper subsets of the set {1, 2, 3} is.
6
124 - The power set P((A × B) ∪ (B × A)) has the same number of elements as the power set P((A × B) ∪ (A × B)) if and only if
A = ∅ or B = ∅ or A = B
125 - The range of the function f(x) = │x – 1│ is
[0, ∞)
126 - The range of the function f(x) = x / │x│ is
{-1, 1}
127 - The set (A U B U C) ? (A ? B’ ? C’)’ ? C’ is equal to
B?C'
128 - The set of all Equivalence classes of a set A of cardinality C
forms a partition of A
129 - The set of all real numbers under the usual multiplication operation is not a group since
zero has no inverse
130 - The set of intelligent students in a class is.
Not a well defined collection
131 - The smallest set A such that A ∪ {1, 2} = {1, 2, 3, 5, 9} is
{3, 5, 9}
132 - The union of sets A and B is expressed as ?
AUB
133 - The universal relation A x A on A is
an equivalence relation
134 - To draw general conclusions from well known facts is called
Induction
135 - Total number of diferent partitions of a set having four elements is
15
136 - Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are respectively
6, 3
137 - Two finite sets have n and m elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then the values of m and n are
6, 4
138 - Which of the following are true:
1 and 2
139 - Which of the following does not have a proper subset
{x: x ? N, 3 < x < 4}
140 - Which of the following is not correct?
All of these
141 - Which of the following sets are null sets ?
Both (a) and (b)
142 - Which of the following statements is false ?
If R, R' are reflexive relations in A, then R - R' is reflexive
143 - Which of the following statements is FALSE?
A − (B ∪ C) = (B − C) − A
144 - Which of the following statements is true?
Number of relations form A = {x, y, z} to B= {1, 2} is 64.
145 - Which of the following statements is TRUE?
For all sets A, B, and C, (A − B) ∩ (C − B) = (A ∩ C) − B.
Pages
No comments:
Post a Comment
Your Valued Comments Help us to improve our site. Thanks