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

Define binary operations on sets?

Important Questions on Set Theory and Relations

EASY

Mathematics>Algebra>Set Theory and Relations>Binary Operations

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>Binary Operations

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

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Binary Operations

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>Binary Operations

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>Set Theory and Relations>Binary Operations

A = \{a, b, c\}

, then the number of binary operations on

A

EASY

Mathematics>Algebra>Set Theory and Relations>Binary Operations

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

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Binary Operations

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>Binary Operations

Let

⊙

be a binary opertation on

ℚ - \{0\}

defined by a

⊙ b = \frac{a}{b}

. Then

1 ⊙ (2 ⊙ (3 ⊙ 4))

is equal to

EASY

Mathematics>Algebra>Set Theory and Relations>Binary Operations

Let* be a binary operation on the set

R

of real numbers defined by

a^{*} b = \frac{3 a b}{7}

, then the identity element in

R

for

^{*}

EASY

Mathematics>Algebra>Set Theory and Relations>Binary Operations

The number of binary operations on the set

{1, 2, 3}

EASY

Mathematics>Algebra>Set Theory and Relations>Binary Operations

Let

A = \{0, 3, 4, 6, 7, 8, 9, 10\}

and

R

be the relation defined on

A

such that

R \{(x, y) \in A \times A : x - y is odd positive integer or x - y = 2\}

. The minimum number of elements that must be added to the relation

R,

so that it is a symmetric relation, is equal to

_________

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Binary Operations

For the binary operation

*

defined on

R - \{1\}

by the rule

a * b = a + b + a b

for all

a, b \in R - \{1\}

, the inverse of

a

EASY

Mathematics>Algebra>Set Theory and Relations>Binary Operations

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}\}

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Binary Operations

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

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Binary Operations

Among the two statements

$(S_{1}) : (p \Rightarrow q) \land (p \land (~ q))$ is a contradiction and $(S_{2}) : (p \land q) \lor ((~ p) \land q) \lor (p \land (~ q)) \lor ((~ p) \land (~ q))$ is a tautology

EASY

Mathematics>Algebra>Set Theory and Relations>Binary Operations

Define identity element for a binary operation defined on a set.

EASY

Mathematics>Algebra>Set Theory and Relations>Binary Operations

The identity element of the binary operation

*

R

defined by

a * b = \frac{a b}{4} \forall a, b \in R

EASY

Mathematics>Algebra>Set Theory and Relations>Binary Operations

Let

*

be a binary operation on the set

R

, of all real numbers defined by

5 (a^{*} b) = a b

, for all

a, b \in R

. The inverse of

0.5

under the operation

*

MEDIUM

Mathematics>Algebra>Set Theory and Relations>Binary Operations

*

is a binary operation defined by

a * b = \frac{a}{b} + \frac{b}{a} + \frac{1}{a b}

for positive integers

a

and

b

, then

2 * 5

is equal to

EASY

Mathematics>Algebra>Set Theory and Relations>Binary Operations

On the set of positive rationals, a binary operation

*

is defined by

a * b = \frac{2 a b}{5} .

2 * x = 3^{- 1}

then

x =

Define binary operations on sets?

Important Questions on Set Theory and Relations

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