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

If A = { 2 , 4 } , B = { 3 , 4 , 5 } , then ( A ∩ B ) × ( A ∪ B ) =

{ ( 4 , 2 ) , ( 4 , 3 ) , ( 4 , 4 ) , ( 4 , 5 ) }

{ ( 3 , 2 ) , ( 3 , 4 ) , ( 4 , 4 ) , ( 5 , 4 ) }

{ ( 4 , 3 ) , ( 4 , 4 ) , ( 4 , 5 ) }

{ ( 2 , 3 ) , ( 2 , 4 ) , ( 2 , 5 ) }

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

The binary operation * : R × R → R defined by * ( x , y ) = max { x , y } is

both commutative and associative

commutative but not associative

associative but not commutative

neither commutative nor associative

EASY

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If $A = \{1, 2\}$ , then what is the number of relations on $A ?$

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Important Questions on Relations and Functions

MEDIUM

Mathematics>Differential Calculus>Relations and Functions>Types of Relations

Let

A = \{2, 3, 4, 5, \dots ., 30\}

and

' ≃'

be an equivalence relation on

A \times A,

defined by

(a, b) ≃ (c, d),

if and only if

a d = b c

. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair

(4, 3)

is equal to :

EASY

Mathematics>Differential Calculus>Relations and Functions>Types of Relations

Let

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

and

ϕ

denotes null set. If

(A \times B)

denotes cartesian product of the sets

A

and

B

, then

(Y \times A) \cap (Y \times B)

MEDIUM

Mathematics>Differential Calculus>Relations and Functions>Types of Relations

If two sets

A

and

B

have

99

elements in common, then the number of elements common to the sets

A \times B

and

B \times A

EASY

Mathematics>Differential Calculus>Relations and Functions>Types of Relations

A

and

B

are non-singleton sets and

n (A \times B) = 35

. If

B \subset A

, then

{}^{n (A)}C_{n (B)} =

MEDIUM

Mathematics>Differential Calculus>Relations and Functions>Types of 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}

MEDIUM

Mathematics>Differential Calculus>Relations and Functions>Types of Relations

Suppose

P, Q

and

R

are three sets, each with three elements. The number of subsets of the set

P \times Q \times R,

that have at least

2

elements is

EASY

Mathematics>Differential Calculus>Relations and Functions>Types 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}

MEDIUM

Mathematics>Differential Calculus>Relations and Functions>Types of 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.

EASY

Mathematics>Differential Calculus>Relations and Functions>Types of Relations

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

EASY

Mathematics>Differential Calculus>Relations and Functions>Types of Relations

A = {2, 4}, B = {3, 4, 5},

then

(A \cap B) \times (A \cup B) =

EASY

Mathematics>Differential Calculus>Relations and Functions>Types 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.

MEDIUM

Mathematics>Differential Calculus>Relations and Functions>Types 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>Differential Calculus>Relations and Functions>Types 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?

MEDIUM

Mathematics>Differential Calculus>Relations and Functions>Types of Relations

Suppose

A, B

and

C

are three sets, each with three elements. The number of subsets of the set

A \times B \times C

that have at least

2

elements is

EASY

Mathematics>Differential Calculus>Relations and Functions>Types of Relations

Let

R

be the relation in the set

N

given by

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

. Then

MEDIUM

Mathematics>Differential Calculus>Relations and Functions>Types of Relations

The binary operation

* : R \times R \to R

defined by

* (x, y) = \max {x, y}

EASY

Mathematics>Differential Calculus>Relations and Functions>Types 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.

HARD

Mathematics>Differential Calculus>Relations and Functions>Types of Relations

The number of ordered pairs

(a, b)

of positive integers such that

\frac{2 a - 1}{b}

and

\frac{2 b - 1}{a}

are both integers is

EASY

Mathematics>Differential Calculus>Relations and Functions>Types 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

HARD

Mathematics>Differential Calculus>Relations and Functions>Types 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?

If A=1,2, then what is the number of relations on A?

Important Questions on Relations and Functions

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If $A = \{1, 2\}$ , then what is the number of relations on $A ?$