JEE Questions for Maths Sets Relations And Functions Quiz 11 - MCQExams.com

Let X be a family of sets and r be a relation on X defined by A is disjoint from B’. Then R is
  • Reflexive
  • Symmetric
  • Anti – symmetric
  • Transitive
If R is a relation from a set A to set B and S is a relation from B to a seat C, then the relation SoR
  • Is from A to C
  • Is from C to A
  • Does not exist
  • None of these
Let W denote the words in the English dictionary. Define the relation R by : R = {(x, y) ϵ W × W| the words x and y have at least one letter in common}
  • Not reflexive, symmetric and transitive
  • Reflexive, symmetric and not transitive
  • Reflexive, symmetric and transitive
  • Reflexive, not symmetric and transitive
If R be a relation < from A = {1,2,3,4} to B = {1,3,5} i.e. (a, b) ϵ R ⇒ a < b, then RoR–1 is
  • {(1,3), (1,5), (2,3), (2,5),(3,5), (4,5)}
  • {(3,1), (5,1), (3,2), (5,2), (5,3), (5,4)}
  • {(3,3), (3,5), (5,3), (5,5)}
  • {(3,3), (3,4), (4,5)}
A relation from P to Q is
  • A universal set of P × Q
  • P × Q
  • An equivalent set of P × Q
  • A subset of P × Q
Let A = {a,b, c} and B = {1, 2}. Consider a relation R defined from set A to set B. Then R is equal to set
  • A
  • B
  • A × B
  • B × A
On the set N of all natural numbers definite the relation R by aRb if and only if the G.C.D. of a and b is 2, then R is
  • Reflexive, but not symmetric
  • Symmetric only
  • Reflexive and transitive
  • Reflexive, symmetric and transitive
Let R be a relation of the set of integers given by aRb ⇒ a = 2k.b for some integers k. Then R is
  • An equivalence relation
  • Reflexive but not symmetric
  • Reflexive and transitive but not symmetric
  • Reflexive and symmetric but not transitive
Let R be a reflexive relation on a finite set A having n – elements, and let there be m ordered pairs in R. Then
  • m ≥ n
  • m ≤ n
  • m = n
  • None of these
The relation R defined on the set A = {1,2,3,4,5} by R = {(x, y) : | x2 – y2| < 16} is given by
  • {(1,1), (2,1), (3,1), (4,1), (2,3)}
  • {(2,2), (3,2), (4,2), (2,4)}
  • {(3,3), (3,4), (5,4), (4,3), (3,1)}
  • None of these
A relation R is defined from {2,3,4,5} to {3,6,7,10} by xRy ⇒ x is relatively prime to y. Then domain of R is
  • {2,3,5}
  • {3,5}
  • {2,3,4}
  • {2,3,4,5}
Let R be a relation on N defined by R = {(x + y) : x + 2y = 8}. The domain of R is
  • {2,4,8}
  • {2,4,6,8}
  • {2,4,6}
  • {1,2,3,4}
If R = {(x, y)|x, y ϵ Z, x2 + y2 ≤ 4 } is a relation in Z, then domain of R is
  • {0,1,2}
  • {0, –1, –2}
  • {–2,–1,0,1,2}
  • None of these
If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B is
  • 29
  • 92
  • 32
  • 29–1
Let A = {1,2,3} B = {1,3,5}. If relational R from A to B is given by R = {(1, 3), (2, 5), (3,3)}. Then R–1 is
  • {(3,3), (3,1), (5,2)}
  • {(1, 3), (2, 5), (3,3)}
  • {(1,3), (5,2)}
  • None of these
Let R be a reflexive relation on a set A and I be the identity relation on A. Then
  • R ⊂ I
  • I ⊂ R
  • R = 1
  • None of these
Let S be the set of all real numbers. Then the relation R = {(1, b) : + ab > 0} on S is
  • Reflexive and symmetric but not transitive
  • Reflexive and transitive but not symmetric
  • Symmetric, transitive but not reflexive
  • Reflexive, transitive and symmetric
  • None of the above is true
An integer m is said to be related to another integer n if m is a multiple of n. Then the relation is
  • Reflexive and symmetric
  • Reflexive and transitive
  • Symmetric and transitive
  • Equivalence relation
The relation R defined in N as Rb ⇔ b is divisible by a is
  • Reflexive but not symmetric
  • Symmetric but not transitive
  • Symmetric and transitive
  • None of the above
Let R be a relation on set A such that R = R–1 , then R is
  • Reflexive
  • Symmetric
  • Transitive
  • None of these
The relation “is subset of” on the power set P(A) of a set A is
  • Symmetric
  • Anti – symmetric
  • Equivalency relation
  • None of these
The relation R defined on set A is antisymmetric if (a, b) ϵ R ⇒(b,a) ϵ R for
  • Every (a, b) ϵ R
  • No (a, b) ϵ R
  • No (a, b), a ≠ b, ϵ R
  • None of these
In the set A = {1,2,3,4,5} a relation R is defined by R = {(x, y)| x, y ϵ A and x < y}. Then R is
  • Reflexive
  • Symmetric
  • Transitive
  • None of these
Let A be the the non – void set of the children in a family. The relation ‘x’ is a brother of ‘y’ on A is
  • Reflexive
  • Symmetric
  • Transitive
  • None of these
The number of reflexive relations of a set with four elements is equal to
  • 216
  • 2
  • 28
  • 24
The void relation on a set A is
  • Reflexive
  • Symmetric and transitive
  • Reflexive and symmetric
  • Reflexive and transitive
Let R1 be a relation defined by R1 = {(a, b)| a ≥ b, a, b ϵ R}. Then R1 is
  • Reflexive, transitive but not symmetric
  • Reflexive, transitive but not symmetric
  • Symmetric, Transitive but not reflexive
  • Neither transitive nor reflexive but symmetric
Which one of the following relations on R is an equivalence relation ?
  • aR1 b ⇔ |a| = |b|
  • aR2b ⇔ a ≥ b
  • aR3 ⇔ a divides b
  • aR4 ⇔ a < b
If R is an equivalence relation on a set A, then R–1 is
  • Reflexive only
  • Symmetric but not transitive
  • Equivalence
  • None of the above
R is a relation over the set of real numbers and it is given by nm ≥ 0. Then r is
  • Symmetric and transitive
  • Reflexive and symmetric
  • A partial order relation
  • An equivalence relation
In order that a relation R defined on a non – empty set A is an equivalence relation, it is sufficient, if R
  • Is reflexive
  • Is symmetric
  • Is transitive
  • Possesses all the above three properties
A relation “congruence modulo m” is
  • Reflexive only
  • Transitive only
  • Symmetric only
  • An equivalence relation
Solution set of x = 3 (mod 7), P ϵ Z, is given by
  • {3}
  • {7p – 3 : P ϵ Z}
  • {7p + 3 : p ϵ Z}
  • None of these
Let R and S be two equivalence relations on a set A. Then
  • R U S is an equivalence relation on A
  • R ∩ S is an equivalence relation on A
  • R – S is an equivalence relation on A
  • None of the above
Let R and S be two relations on set A. Then
  • R and S are transitive, then R ∪ S is also transitive
  • R and S are transitive, then R ∩ S is also transitive
  • R and S are reflexive, then R ∩ S is also reflexive
  • R and S are symmetric then R ∪ S is also symmetric
  • 2, 3, 4 are Correct
Let R = {(1,3), (2,2), (3,2)} and S = {(2,1), (3,2), (2,3)} be two relations on set A = {1,2,3}. Then RoS =
  • {(1,3), (2,2), (3,2), (2,1), (2,3)}
  • {(3,2), (1,3)}
  • {(2,3), (3,2), (2,2)}
  • {(2,3), (3,2)}
Let L denote the set of all straight lines in a plane. Let a relation R be defined by α R β ⇔ α ⊥ β, α, β ϵ I. Then R is
  • Reflexive
  • Symmetric
  • Transitive
  • None of these
Let R be a relation over the set N × N and it is defined by (a, b) R (c, d) ⇒ a + d = b + c. Then R is
  • Reflexive only
  • Symmetric only
  • Transitive only
  • An equivalence relation
Let n be a fixed positive integer. Define a relation R on the set Z of integers by, a R b ⇔ n |a – b|. Then R is
  • Reflexive
  • Symmetric
  • Transitive
  • Equivalence
  • all the above
Let R = {(3,3), (6, 6), (9, 9), (12,12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on set A = {3,6,9,12}. The relation is
  • An equivalence relation
  • Reflexive and symmetric only
  • Reflexive and transitive only
  • Reflexive only
x2 = xy is a relation which is
  • Symmetric
  • reflexive
  • Transitive
  • None of these
Let R = {(1, 3),(4, 2), (2, 4), (2, 3), (3,1)} be relation on the set A = {1,2,3,4}. The relation R is
  • Reflexive
  • Transitive
  • Not symmetric
  • A function
Let r be a relation from R(set of real numbers) to R defined by r = {(a, b)|a, b ϵ R and a – b + √3 is an irrational number}. The relation r is
  • An equivalence relation
  • Reflexive only
  • Symmetric only
  • Transitive only
Let a relation r in the set N of natural numbers be defined as (x, y) ⇔ x2 – 4xy + 3y2 = 0 ∀ x, y ϵ N. The relation R is
  • Reflexive
  • Symmetric
  • Transitive
  • An equivalence relation
Consider the following relations R = {(x, y)|x, y} are real numbers and x = wy for some rational number w;
Maths-Sets Relations and Functions-50435.png
  • R is an equivalence relation but S is not an equivalence relation
  • Neither R nor S is an equivalence relation
  • S is an equivalence relation but R is not an equivalence relation
  • R and S both are equivalence relation
Let A = {x, y, z} and B = {a,b,c,d}. which one of the following is not a relation from A to B
  • {(x, a), (x, c)}
  • {(y, c), (y, d)}
  • {(z,a), (z, d)}
  • {(z, b), (y, b), (a, d)}
  • {(x, c)}
R ⊆ A × A (where A ≠is an equivalence relation if R is
  • Reflexive, symmetric but not transitive
  • Reflexive, neither symmetric nor transitive
  • Reflexive, symmetric and transitive
  • None of the above
If X = {8n – 7n – 1 : n ϵ N} and Y = {49 (n –: n ϵ N}, then
  • X ⊆ Y
  • Y ⊆ X
  • X = Y
  • None of these
The value of (A ∪ B ∪ C) ∩ (A ∩ Bc ∩ Cc)c ∩ Cc, is
  • B ∩ Cc
  • Bc ∩ Cc
  • B ∩ C
  • A ∩ B ∩ C
Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A ∪ B
  • 3
  • 6
  • 9
  • 18
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