Universal Relations

Q.

For real numbers $xandy,$we write$xRy\Rightarrow x–y+\surd 2$ is an irrational number. Then the relation $R$ is

1. Reflexive

2. Symmetric

3. Transitive

4. None of these

Q.

Find the maximum number of equivalence relations on the set $A=\{1,2,3\}$ .

Q.

If A={a, b, c} , then the relation R={(b, c)}on A is

a reflexive only

b symmetric only

c transitive only

d reflexive and transitive only

Q.

How many elements will be there in the universal relation defined on the set A = {1, 4, 9}

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Q.

Let R be a relation on a finite set A having n elements. Then, the number of relations on A is

1. n²

2. 2^nxn

3. n x n

4. 2ⁿ

Q.

Universal relation on a set A and universal set has same elements

1. True

2. False

Q.

If $A,B$ and $C$ are three finite sets, then what is $\left[\right(A\cup B)\cap C]$equal to?

1. $A\cup B\cap C$

2. $A\cap B\cap C$

3. $A\cap B\cup C$

4. $A\cap B\cap C$

Q. What is a set and list all formulas of set.

Q.

A distance of $180km$ between two cities is represented on a map by $6cm$. If the distance between two other towns is represented by $5cm$ on the map, what is the actual distance between them $?$

Q.

Let $I$ be the set of integers and $R$ be a relation on $I$ defined by $R=\left\{\right(x,y):(x-y)isdivisibleby11,x,y\in I\}$. Then $R$ is

1. An equivalence relation

2. Symmetric only

3. Reflexive only

4. Transitive only

Q.

Which of the following relations are equivalent?

1. Let two people be related if and only if they are friends

2. Let two people be related if and only if they are either the same person, siblings, or half-siblings

3. Empty relation defined on the set A = {1}

4. Universal relation defined on the set of integers satisfying |x|<5

Q. If a relation $R$ is defined on $A=\{1,2,3,4\}$, then which of the following is/are universal relation?

1. $R=\left\{\right(a,b):a+b<10:a,b\in A\}$
2. $R=\left\{\right(a,b):\text{value of}a-b\text{is an integer}:a,b\in A\}$
3. $R=\left\{\right(a,b):\text{value of}\frac{a}{b}\text{is an integer}:a,b\in A\}$
4. $R=\left\{\right(a,b):ab\text{is a real number}:a,b\in A\}$

Q. If a relation $R$ is defined on $A=\{1,2,3,4\}$, then which of the following is/are universal relation?

1. $R=\left\{\right(a,b):a+b<10:a,b\in A\}$
2. $R=\left\{\right(a,b):\text{value of}a-b\text{is an integer}:a,b\in A\}$
3. $R=\left\{\right(a,b):\text{value of}\frac{a}{b}\text{is an integer}:a,b\in A\}$
4. $R=\left\{\right(a,b):ab\text{is a real number}:a,b\in A\}$

Q.

Indicate each of the following statements by appropriate integers:

$9°C$ below $0°C$

Q.

Suppose $y$ varies jointly as $x$ and $z$.

How do you find $y$ when $x=6$ and $z=8$, if $y=6$ when $x$ is $4$ and $z$ is $2$?

Q.

How many elements will be there in the universal relation defined on the set A = {1, 4, 9}

___

Q.

Universal relation on a set A and universal set has same elements

1. True

2. False

Q. If f : A → B and g : B → C are onto functions, show that gof is a onto function.

Q.

How many elements will be there in the universal relation defined on the set A = {1, 4, 9}

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Q. Let $A$ and $B$ be two sets in the same universal set. Then, $A-B=$

1. $A\cap B$
2. $A\cap B^{\prime }$
3. None of these
4. $A^{\prime }\cap B$

Q.

Classify the set of members of ‘SAARC’ association as finite or infinite set.

Q.

Universal relation on set A and Cartesian product A $\times$ A has the same elements

1. True

2. False

Q.

A relation which has all the elements of set A is called universal relation on set A

1. True

2. False

Q.

Let the relation $R$ defined on the set of natural numbers $N$ be : $R=\left\{\left(a,b):bisdivisibleby\forall a,b\in N\right)\right\}$ Then $R$ is

1. Reflexive and symmetric only

2. Symmetric and transitive only

3. Reflexive and transitive only

4. An equivalence relation

Q.

what is function

Q.

List the elements of $A\cap B$, if $\mathrm{A}=\{\mathrm{x}\mid \mathrm{x}+3=0,\mathrm{x}\in \mathrm{\mathbb{N}}\},\mathrm{B}=\{\mathrm{x}\mid \mathrm{x}\le 3,\mathrm{x}\in \mathrm{W}\}$.

Q.

Universal relation on set A and Cartesian product A $\times$ A has the same elements

1. True

2. False

Q. In a universal relation, every element of set A is related to every element of set A

1. True
2. False

Q.

How many elements will be there in the universal relation defined on the set A = {1, 4, 9}

___

Q.

Universal relation on a set A and universal set has same elements

1. False

2. True