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

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 ) }

If A = x / x ≤ 10 , x ∈ N and B = x / x ≤ 10 , x ∈ W , then A ∩ B = ?

1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10

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Which one of the following statements is/are correct for the 'Reflexive relation'?

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Important Questions on Relations and Functions

EASY

Mathematics>Algebra>Relations and Functions>Basics of 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

MEDIUM

Mathematics>Algebra>Relations and Functions>Basics of 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>Basics of 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 ?

EASY

Mathematics>Algebra>Relations and Functions>Basics of 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>Basics of 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

EASY

Mathematics>Algebra>Relations and Functions>Basics of 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>Basics of 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>Basics of 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>Basics of 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

MEDIUM

Mathematics>Algebra>Relations and Functions>Basics of 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>Basics of 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>Basics of Relations

In a group of boys,

25

play volleyball,

20

play badminton and

10

boys play cricket. Five boys play all the three games. 8 boys play atleast two of the three games. How many of them play only one game?

EASY

Mathematics>Algebra>Relations and Functions>Basics of 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>Basics of Relations

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

EASY

Mathematics>Algebra>Relations and Functions>Basics of 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>Basics of 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.

MEDIUM

Mathematics>Algebra>Relations and Functions>Basics of 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

EASY

Mathematics>Algebra>Relations and Functions>Basics of 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>Basics of Relations

If $A = \{x / x \leq 10, x \in N\}$ and $B = \{x / x \leq 10, x \in W\}$ , then $A \cap B = ?$

HARD

Mathematics>Algebra>Relations and Functions>Basics of Relations

In an examination

51 %

students fail in English and

45 %

fail in Maths. If

21 %

students fail in both the subjects, then

169

students pass the examination. What is the total number of students taking the exam?

Which one of the following statements is/are correct for the 'Reflexive relation'?

Important Questions on Relations and Functions

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