A relation R is defined in the set Z of integers as follows x , y ∈ R if and only if x 2 + y 2 = 9 . Which of the following is false?

R = 0 , 3 , 0 , − 3 , 3 , 0 , − 3 , 0

Determine the relation R on the set of whole numbers ≤ 10 defined by R = { ( x , y ) ∣ 2 x + 3 y = 12 } .

Given, R = ( x , y ) ; 2 x + 3 y = 12 , { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 910 } x = 0 , 2 × 0 + 3 y = 12 ⇒ y = 4 ⇒ ( 0 , 4 ) x = 1 , 2 × 1 + 3 y = 12 ⇒ y = 10 3 x = 2 , 2 × 2 + 37 = 12 ⇒ y = 8 3 x = 3 , 2 × 3 + 3 y = 12 ⇒ y = 2 ⇒ ( 3 , 2 ) x = 4 , 2 × 4 + 3 y = 12 ⇒ y = 4 3 x = 5 , 2 × 5 + 3 y = 12 ⇒ y = 2 3 x = 6 , 2 × 6 + 3 y = 12 ⇒ y = 0 ⇒ ( 6 , 0 ) ∴ R = { ( 0 , 4 ) , ( 3 , 2 ) , ( 6 , 0 ) }

Let N denote the set of all natural numbers. Define two binary relations on N as R 1 = x , y ∈ N × N : 2 x + y = 10 and R 2 = x , y ∈ N × N : x + 2 y = 10 . Then

both R 1 and R 2 are transitive relations

both R 1 and R 2 are symmetric relations

EASY

Earn 100

Set $A = \{1, 2, 3, 4, 5\}$ , set $B = \{1, 8, 27, 64, 125\}$

Write a relation in set-builder form to represent the relation above.

Important Questions on Relations and Functions

EASY

Mathematics>Algebra>Relations and Functions>Relations

Let

R

be the relation in the set

N

given by

R = {(a, b) : a = b - 2, b > 6}

. Then

EASY

Mathematics>Algebra>Relations and Functions>Relations

If set

A = {x : x is a measure of an angle of scalen triangle}

, then the number of relation containing (measure of minimum angle, measure of maximum angle) is

EASY

Mathematics>Algebra>Relations and Functions>Relations

A relation

R

is defined in the set

Z

of integers as follows

(x, y) \in R

if and only if

x^{2} + y^{2} = 9

. Which of the following is false?

EASY

Mathematics>Algebra>Relations and Functions>Relations

Let

A = \{2, 3, 4\}

and

B = \{8, 9, 12\}

. Then the number of elements in the relation

R = \{((a_{1}, b_{1}), (a_{2}, b_{2})) \in (A \times B, A \times B) : a_{1} divides b_{2} and a_{2} divides b_{1}\}

EASY

Mathematics>Algebra>Relations and Functions>Relations

Consider the following relations in the real numbers

R_{1} = \{(x, y) ∣ x^{2} + y^{2} \leq 25\}

and

R_{2} = \{(x, y), y \geq \frac{4 x^{2}}{9}\}

, then the range of

R_{1} \cap R_{2}

EASY

Mathematics>Algebra>Relations and Functions>Relations

Let

A = \{1, 2, 3, 4, 5\}

and let

B = \{1, 2, 3, 4\}

. If the relation

R : A \to B

is given by

(a, b) \in R

if and only if

a + b

is even, then

n (R)

is equal to

EASY

Mathematics>Algebra>Relations and Functions>Relations

Let $R$ be the relation on the set $N$ given by $R = {(a, b) : a = b - 2, b > 6}$ . Choose the correct answer.

MEDIUM

Mathematics>Algebra>Relations and Functions>Relations

Let

A = {x : 1 < x < 10, x is an odd natural number}

and

B = {y : 90 < y < 100, y is a prime number}

. Write the number of relations from

A

B

MEDIUM

Mathematics>Algebra>Relations and Functions>Relations

Let

A

be a set consisting of

10

elements. The number of non-empty relations from

A

A

that are reflexive but not symmetric is

EASY

Mathematics>Algebra>Relations and Functions>Relations

Let

A, B, C

are three non-empty sets. The number of relations from

A

B

64

, that of

B

C

4096

and that of

A

C

256

. Then the numbers of elements of the sets are in

EASY

Mathematics>Algebra>Relations and Functions>Relations

Determine the relation $R$ on the set of whole numbers $\leq 10$ defined by $R = {(x, y) ∣ 2 x + 3 y = 12}$ .

EASY

Mathematics>Algebra>Relations and Functions>Relations

Let

A = {2, 3, 4, 5}, B = {36, 45, 49, 60, 77, 90}

and let

R

be the relation 'is factor of' from

A

B

. Then the range of

R

is the set

EASY

Mathematics>Algebra>Relations and Functions>Relations

Sets $A and B$ have respectively $m and n$ elements. The total number of relations from $A to B is 64$ . If $m < n and m \neq 1$ , write the values of $m and n$ respectively.

EASY

Mathematics>Algebra>Relations and Functions>Relations

Let

R

be a relation in the set

N

of natural numbers given by

R = {(a, b) : a = b - 2}

. Choose the correct answer.

MEDIUM

Mathematics>Algebra>Relations and Functions>Relations

Consider the set of real numbers $R$ . Define the relation $R$ on $R$ as " $a R b$ if and only if $a^{2} + b^{2} = 1$ . Write the domain of $R$ . Also, prove that $R$ is not transitive.

MEDIUM

Mathematics>Algebra>Relations and Functions>Relations

R = \{(x, y) : x, y \in Z, x^{2} + 3 y^{2} \leq 8\}

is a relation on the set of integers

Z

, then the domain of

R^{- 1}

EASY

Mathematics>Algebra>Relations and Functions>Relations

Let

A = \{0, 3, 4, 6, 7, 8, 9, 10\}

and

R

be the relation defined on

A

such that

R \{(x, y) \in A \times A : x - y is odd positive integer or x - y = 2\}

. The minimum number of elements that must be added to the relation

R,

so that it is a symmetric relation, is equal to

_________

EASY

Mathematics>Algebra>Relations and Functions>Relations

If there are

2

elements in a set

A,

then what would be the number of possible relations from the set

A

to set

A ?

MEDIUM

Mathematics>Algebra>Relations and Functions>Relations

n (A) = 2

and total number of possible relations from set

A

to set

B

1024

, then

n (B)

EASY

Mathematics>Algebra>Relations and Functions>Relations

Let

N

denote the set of all natural numbers. Define two binary relations on

N

R_{1} = \{(x, y) \in N \times N : 2 x + y = 10\}

and

R_{2} = \{(x, y) \in N \times N : x + 2 y = 10\}

. Then

Set A=1,2,3,4,5 , set B=1,8,27,64,125 Write a relation in set-builder form to represent the relation above.

Important Questions on Relations and Functions

Learn and Prepare for any exam you want !

Set $A = \{1, 2, 3, 4, 5\}$ , set $B = \{1, 8, 27, 64, 125\}$

Write a relation in set-builder form to represent the relation above.