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 ) }

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

$A = \{p, q\}$ , $B = \{q, r\}$ and $C = \{p, r\}$ . Verify associative property of Cartesian product of sets.

Important Questions on Set Theory and Relations

MEDIUM

Mathematics>Algebra>Set Theory and Relations>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>Set Theory and Relations>Basics 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>Algebra>Set Theory and Relations>Basics 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

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Basics 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

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Basics 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}

EASY

Mathematics>Algebra>Set Theory and Relations>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>Set Theory and Relations>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>Set Theory and Relations>Basics 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>Algebra>Set Theory and Relations>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>Set Theory and Relations>Basics of Relations

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

then

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

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Basics 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>Algebra>Set Theory and Relations>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>Set Theory and Relations>Basics of Relations

A

and

B

are two non-empty finite sets having

3

and

4

elements respectively, then what would be the number of ordered pairs in

A \times B ?

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Basics 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>Algebra>Set Theory and Relations>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 ?

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Basics of Relations

Let

R_{1}

and

R_{2}

be relations on the set

\{1, 2, \dots, 50\}

such that

R_{1} =

{

(p, p^{n}) : p

is a prime and

n \geq 0

is an integer} and

R_{2} =

{

(p, p^{n}) : p

is a prime and

n = 0

1

}. Then, the number of elements in

R_{1} - R_{2}

is ____.

EASY

Mathematics>Algebra>Set Theory and Relations>Basics of Relations

Let

x \times y = x^{2} + y^{3}

and

(x \times 1) \times 1 = x \times (1 \times 1)

. Then a value of

2 \sin^{- 1} (\frac{x^{4} + x^{2} - 2}{x^{4} + x^{2} + 2})

HARD

Mathematics>Algebra>Set Theory and Relations>Basics 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>Algebra>Set Theory and Relations>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>Set Theory and Relations>Basics of Relations

Let

A

and

B

be two sets containing

2

elements and

4

elements respectively. The number of subsets of

A \times B

having

3

or more elements is :

A=p,q, B=q,r and C=p,r. Verify associative property of Cartesian product of sets.

Important Questions on Set Theory and Relations

Learn and Prepare for any exam you want !

$A = \{p, q\}$ , $B = \{q, r\}$ and $C = \{p, r\}$ . Verify associative property of Cartesian product of sets.