Let R be a relation on the set L of lines dened by l1 R l2 if l1 is perpendicular to l2 , then relation R is
reflexive and symmetric
symmetric and transitive
equivalence relation
symmetric
Given set A ={1,2,3} and a relation R={(1,2),(2,1)}, the relation R will be
Reflexive if (1,1) is added
Symmetric if (2,3) is added
Transitive if (1,1) is added
Symmetric if (3,2) is added
Given set A = {a, b, c). An identity relation in set A is
R = {(a, b), (a, c)}
R = {(a, a), (b, b), (c, c)}
R = {(a, a), (b, b), (c, c), (a, c)}
R= {(c, a), (b, a), (a, a)}
If A and B are two given sets, then A∩(A∩B)ⁿ is equal to
A
B
φ
A∩Bⁿ
If a set A has n elements, then the total number of subsets of A is
n
n²
2ⁿ
2n
If A and B are any two sets, then A∪(A∩B)is equal to
A
B
Aⁿ
Bⁿ
The number of proper subsets of the set {1, 2, 3} is
8
7
6
5
if each element of A is related to every element of A, i.e., R = A × A.
empty relation
universal relation
equivalence relation
symmetric
Given the sets A={1,2,3},B={3,4}, C = {4, 5, 6}, then A∪(B∩C) is
{3}
{1, 2, 3, 4}
{1, 2, 4, 5}
{1, 2, 3, 4,5,6}
A relation R in a set A is called _______, if (a, a) ∈ R, for every a ∈ A,
reflexive
symmetric
transitive
All of the above
A relation R in a set A is called_________ , if (a1, a2) ∈ R implies that (a2, a1) ∈ R, for all a1, a2 ∈ A.
reflexive
symmetric
transitive
All of the above
A relation R in a set A is called_________ , if (a1, a2) ∈ R and (a2, a3) ∈ R implies that (a1, a3)∈ R, for all a1, a2,a3 ∈ A.
reflexive
symmetric
transitive
All of the above
The set A={x:x∈R,x²=16 and 2x=6} equals
φ
{14, 3, 4}
{3}
{4}
A function f : X → Y is said to be ________, if every element of Y is the image of some element of X under f, i.e., for every y ∈ Y, there exists an element x in X such that f(x) = y
injective
surjective
bijective
None
A function f : X → Y is said to be _________, if f is both one-one and onto.
injective
surjective
bijective
None
Let f : R → R be defined as f(x) = x^4. Choose the correct answer
f is one-one onto
f is many-one onto
f is one-one but not onto
f is neither one-one nor onto.
Let f : R → R be defined as f(x) = 3x. Choose the correct answer.
f is one-one &onto
f is many-one onto
f is one-one but not onto
f is neither one-one nor onto.
Let S={0,1,5,4,7}. Then the total number of subsets of S is
64
32
40
20
If A={a,b},B={c,d},C={d,e}, then{(a,c),(a,d),(a,e),(b,c),(b,d),(b,e)} is equal to
A ∩ (B ∪ C)
A ∪ (B ∩ C)
A × (B ∪ C)
A × (B ∩ C)
An element a ∈ X is _________ for binary operation ∗ : X × X → X, if there exists b ∈ X such that a ∗ b = e = b ∗ a
commutative
associative
invertible
None
Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is
1
2
3
4
Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is
1
2
3
4
Let n(U)=700,n(A)=200,n(B)=300 and n(A∩B)=100, then n(Aⁱ∩Bⁱ)=
400
3300
2900
1400
If A, B and C are any three sets, then A × (B ∪ C) is equal to