Sets, Relations and Functions Test

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Sets, Relations and Functions Test - 57

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Weekly Quiz Competition

Question 1
4 / -1

Let R be a relation on set A such that R = R^–1 , then R is

A
Reflexive

B
Symmetric

C
Transitive

D
None of these

Solution
Question 2
4 / -1

Let R = {(a, a)} be a relation on set A. Then r is

A
Symmetric

B
Antisymmetric

C
Symmetric and antisymmetric

D
Neither symmetric nor anti – symmetric
Question 3
4 / -1

The relation “is subset of” on the power set P(A) of a set A is

A
Symmetric

B
Anti – symmetric

C
Equivalency relation

D
None of these
Question 4
4 / -1

The relation R defined on set A is antisymmetric if (a, b) ϵ R ⇒(b,a) ϵ R for

A
Every (a, b) ϵ R

B
No (a, b) ϵ R

C
No (a, b), a ≠ b, ϵ R

D
None of these
Question 5
4 / -1

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

A
Reflexive

B
Symmetric

C
Transitive

D
None of these

Solution
Question 6
4 / -1

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

A
Reflexive

B
Symmetric

C
Transitive

D
None of these
Question 7
4 / -1

The number of reflexive relations of a set with four elements is equal to

A
2¹⁶

B
2

C
2⁸

D
2⁴

Solution
Question 8
4 / -1

The void relation on a set A is

A
Reflexive

B
Symmetric and transitive

C
Reflexive and symmetric

D
Reflexive and transitive
Question 9
4 / -1

Let R₁ be a relation defined by R₁ = {(a, b)| a ≥ b, a, b ϵ R}. Then R₁ is

A
Reflexive, transitive but not symmetric

B
Reflexive, transitive but not symmetric

C
Symmetric, Transitive but not reflexive

D
Neither transitive nor reflexive but symmetric
Question 10
4 / -1

Which one of the following relations on R is an equivalence relation ?

A
aR₁ b ⇔ |a| = |b|

B
aR₂b ⇔ a ≥ b

C
aR₃ ⇔ a divides b

D
aR₄ ⇔ a < b

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Re-Attempt Weekly Quiz Competition

Sets, Relations and Functions Test - 57

Result

Sets, Relations and Functions Test - 57

Score

-

Rank

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SHARING IS CARING

Question 1

Reflexive

Symmetric

Transitive

None of these

Solution

Question 2

Symmetric

Antisymmetric

Symmetric and antisymmetric

Neither symmetric nor anti – symmetric

Question 3

Symmetric

Anti – symmetric

Equivalency relation

None of these

Question 4

Every (a, b) ϵ R

No (a, b) ϵ R

No (a, b), a ≠ b, ϵ R

None of these

Question 5

Reflexive

Symmetric

Transitive

None of these

Solution

Question 6

Reflexive

Symmetric

Transitive

None of these

Question 7

216

2

28

24

Solution

Question 8

Reflexive

Symmetric and transitive

Reflexive and symmetric

Reflexive and transitive

Question 9

Reflexive, transitive but not symmetric

Reflexive, transitive but not symmetric

Symmetric, Transitive but not reflexive

Neither transitive nor reflexive but symmetric

Question 10

aR1 b ⇔ |a| = |b|

aR2b ⇔ a ≥ b

aR3 ⇔ a divides b

aR4 ⇔ a < b

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2¹⁶

2⁸

2⁴

aR₁ b ⇔ |a| = |b|

aR₂b ⇔ a ≥ b

aR₃ ⇔ a divides b

aR₄ ⇔ a < b