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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If $f (x) = 1 / 1 - x, f (- 1)$ is

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Important Questions on Relations and Functions

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Mathematics>Algebra>Relations and Functions>Basics of Relations

Let

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and

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

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Mathematics>Algebra>Relations and Functions>Basics of Relations

A relation

R

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(x, y) \in R

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

. Which of the following is false?

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Mathematics>Algebra>Relations and Functions>Basics of Relations

Let

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B

64

, that of

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C

4096

and that of

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Mathematics>Algebra>Relations and Functions>Basics of Relations

Let

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

and let

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A

B

. Then the range of

R

is the set

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n (A) = 2

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to set

B

1024

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Mathematics>Algebra>Relations and Functions>Basics of Relations

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Mathematics>Algebra>Relations and Functions>Basics of Relations

In a group of boys,

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play badminton and

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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

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Mathematics>Algebra>Relations and Functions>Basics of Relations

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Mathematics>Algebra>Relations and Functions>Basics of Relations

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Mathematics>Algebra>Relations and Functions>Basics of Relations

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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\}

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

, then the range of

R_{1} \cap R_{2}

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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

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169

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

If f(x)=1/1-x, f(-1) is

Important Questions on Relations and Functions

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If $f (x) = 1 / 1 - x, f (- 1)$ is