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

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

MEDIUM

Earn 100

Out of $60$ students in a class, $15$ fail in English and $13$ fail in Hindi. If $4$ students fail both in Hindi and English. Then the number of students who pass in both the subjects is

50% studentsanswered this correctly

Important Questions on Sets, Relations and Functions

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and 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>Algebra>Sets, Relations and Functions>Sets and 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>Algebra>Sets, Relations and Functions>Sets and 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>Algebra>Sets, Relations and Functions>Sets and Relations

A

and

B

are non-singleton sets and

n (A \times B) = 35

. If

B \subset A

, then

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

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and 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>Sets, Relations and Functions>Sets and 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>Algebra>Sets, Relations and Functions>Sets and 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>Algebra>Sets, Relations and Functions>Sets and 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>Sets, Relations and Functions>Sets and 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>Sets, Relations and Functions>Sets and Relations

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

then

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

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and 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>Sets, Relations and Functions>Sets and 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>Sets, Relations and Functions>Sets and 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>Algebra>Sets, Relations and Functions>Sets and 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>Algebra>Sets, Relations and Functions>Sets and Relations

Let

R

be the relation in the set

N

given by

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

. Then

MEDIUM

Mathematics>Algebra>Sets, Relations and Functions>Sets and Relations

The binary operation

* : R \times R \to R

defined by

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

EASY

Mathematics>Algebra>Sets, Relations and Functions>Sets and 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>Algebra>Sets, Relations and Functions>Sets and 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>Algebra>Sets, Relations and Functions>Sets and 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>Sets, Relations and Functions>Sets and 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?

Out of 60 students in a class, 15 fail in English and 13 fail in Hindi. If 4 students fail both in Hindi and English. Then the number of students who pass in both the subjects is

Important Questions on Sets, Relations and Functions

Learn and Prepare for any exam you want !

Out of $60$ students in a class, $15$ fail in English and $13$ fail in Hindi. If $4$ students fail both in Hindi and English. Then the number of students who pass in both the subjects is