Reflexive Relations

Q.

Let m be a given fixed positive integer.

Let $R=\left\{\right(a,b):a,bϵZ\}\text{and}(a-b)\text{is divisible by m}$

Show that R is an equivalence relation on Z.

Q. If a relation $R$ is defined on set of real numbers as $xRy⟺x-y+\sqrt{2}$ is an irrational number, then the relation $R$ is

1. a reflexive relation
2. a symmetric relation
3. a transitive relation
4. both reflexive and transitive relation

Q.

The side of a regular pentagon is denoted by l. Express the perimeter of the pentagon using l.

Q. If $A=\{1,2,3\},$ then number of reflexive relations that can be defined on $A$ is

Q. R is relation over the set of integers and it is given by (x, y) $ϵ$ R $\iff$ R |x - y| $\le$ 1. Then, R is

1. Reflexive and transitive
2. reflexive and symmetric
3. Symmetric and transitive
4. an equivalence relation

Q.

Let R be a relation on the set N be defined by {(x, y)| x, y Î N, 2x + y = 41}. Then R is

1. Reflexive

2. Symmetric

3. Transitive

4. None of these

Q. Paragraph for below question

नीचे दिए गए प्रश्न के लिए अनुच्छेद

Consider a function f(x) = {2x}, where {·} represents fractional part function.

फलन f(x) = {2x} पर विचार कीजिए, जहाँ {·} भिन्नात्मक भाग फलन को दर्शाता है।

Q. The fundamental period of f(x) is equal to

प्रश्न - f(x) के मूल आवर्तकाल का मान बराबर है

1. 1
2. 2
3. $\frac{1}{2}$
4. $\frac{1}{4}$

Q. Let $R$ be a reflexive relation on finite set $A$ having $n-$elements, and let there be $m-$ordered pairs in $R.$ Then

1. $m\ge n$
2. $m\le n$
3. $m=n$
4. Relation between $m\text{and}n$ cannot be determined.

Q. Let R be the relation on the set of all real numbers defined by a R b iff $|a-b|\le 1$. Then R is

1. Reflexive and Symmetric
2. Symmetric only
3. Transitive only
4. Anti-symmetric only

Q. Let a relation R in the set R of real numbers be defined as (a, b) $ϵ$ R if and only if 1 + ab > 0 for all a, b $ϵ$ R. The
relation R is

1. Reflexive and symmetric
2. symmetric and transitive
3. an equivalence relation
4. None of these

Q.

Let R be the realtion on the set R of all real

numbers defined by a R b if |a-b| $\le$ 1. then R is

1. Reflexive and Symmetric

2. Symmetric only

3. Transitive only

4. Anti-symmetric only

Q. For real numbers x and y, we write $xRy\iff x-y+\sqrt{2}$ is an irrational number. Then the relation R is

1. Reflexive

2. Symmetric

3. Transitive

4. None of these

Q. Let a relation $R$ on the set $N$ of natural numbers be defined as $(x,y)\iff x^2-4xy+3y^2=0\forall x,y\in N.$ Then the relation $R$ is

1. reflexive
2. symmetric
3. transitive
4. an equivalence relation

Q.

The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is

1. Reflexive but not symmetric

2. Reflexive but not transitive

3. Neither symmetric nor transitive

4. Symmetric and Transitive

Q. Let f : R → [ln 4, ∞) be defined by f(x) = ln(x² + 4), then f(x) is

माना f : R → [ln 4, ∞), f(x) = ln(x² + 4) द्वारा परिभाषित है, तब f(x) है

1. Not a function
   
   एक फलन नहीं
2. A one-one function
   
   एक एकैकी फलन
3. An into function
   
   एक अंतःर्क्षेपी फलन
4. An onto function
   
   एक आच्छादक फलन