Relations and Functions Test

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Relations and Functions Test - 8

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Weekly Quiz Competition

Question 1
1 / -0

If R is a relation from a set A to a set B and S is a relation from B to C, then the relation S ∘ R.

A
Is from A to C

B
Is from C to A

C
Is from A to B

D
does not exist

Solution

Let R and S be two relations from sets A to B and B to C respectively.Then we can define a relation S ∘ R

from A to C such that (a,c) ∈ S ∘ R this relation is called the composition of R and S.
Question 2
1 / -0

The binary operation * defined on the set of integers as a∗ b = |a − b| −1 is:

A
Associative

B
Commutative

C
Not commutative

D
Both commutative and associative

Solution

Here * is commutative as b * a = |b − a| −1 = |a − b| − 1 = a ∗ b.Because ,|−x| = |x| for all x ∈ R .
Question 3
1 / -0

R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation R⁻¹=

A
{(8, 11), (9, 12), (10, 13)}

B
{(8, 11), (10, 13)}

C
{(8,11),(10,13),(12,15)}

D
{(11, 8), (13, 10)}

Solution

R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation R⁻¹ is given by x = y + 3, from {8, 10, 12} to { 11, 12, 13} ⇒ relation = {(8,11),(10,13)}.
Question 4
1 / -0

Given the relation R = {(1, 2), (2, 3)} on the set {1, 2, 3}, the minimum number of ordered pairs which when added to R make it an equivalence relation is =

A
8

B
5

C
6

D
7

Solution

To make the relation an equivalence relation , the following ordered pairs are required (1,1),(2,2),(3,3)(2,1)(3,2)(1,3),(3,1).
Question 5
1 / -0

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1),(3,2)} be a relation on the set A = {1, 2, 3, 4}. The relation R is

A
transitive

B
reflexive

C
symmetric

D
non symmetric

Solution

R is said to be symmetric if (a,b) ∈ R ⇒ (b,a) ∈ R ,here (1,3) ∈ R ⇒ (3,1) ∈ R etc.
Question 6
1 / -0

In Z , the set of integers, inverse of – 7 , w.r.t. ‘ * ‘ defined by a * b = a + b + 7 for all a, b ∈ Z ,is

A
-14

B
7

C
-7

D
14

Solution

If ‘ e ‘ is the identity ,then a*e = a ⇒ a + e + 7 = a ⇒ e = - 7 . Also,inverse of e is e itself. Hence , inverse of -7 is -7.
Question 7
1 / -0

A Relation is a

A
universal set

B
power set

C
Cartesian product of two sets

D
null set

Solution

By definition of Relation, : A relation from a non-empty set A to a non empty set B is a subset of A x B . If ( x, y) ∈ R , then we write xRy and we say that x is related to y through R.
Question 8
1 / -0

A relation R on a set A is called an empty relation if

A
every element of A is related to one element of A

B
every element of A is related to any element of A

C
one element of A is related to all the elements of A

D
no element of A is related to any element of A

Solution

For any set A ,an empty relation may be defined on A as: there is no element exists in the relation set which satisfies the relation for a given set A i.e.

let A={1,2,3,4,5} and R={(a,b): a,b ∈ A and a+b= 10},so we get R={ } which is an empty relation.

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Re-Attempt Weekly Quiz Competition

Relations and Functions Test - 8

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Relations and Functions Test - 8

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Question 1

Is from A to C

Is from C to A

Is from A to B

does not exist

Solution

Question 2

Associative

Commutative

Not commutative

Both commutative and associative

Solution

Question 3

{(8, 11), (9, 12), (10, 13)}

{(8, 11), (10, 13)}

{(8,11),(10,13),(12,15)}

{(11, 8), (13, 10)}

Solution

Question 4

8

5

6

7

Solution

Question 5

transitive

reflexive

symmetric

non symmetric

Solution

Question 6

-14

7

-7

14

Solution

Question 7

universal set

power set

Cartesian product of two sets

null set

Solution

Question 8

every element of A is related to one element of A

every element of A is related to any element of A

one element of A is related to all the elements of A

no element of A is related to any element of A

Solution

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