What is Relation?

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What is Relation?

AnjaliYadav Asked Jun 16, 2021 recategorized Jul 31, 2023 by ALOK_RAJ

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Chandan Asked Sep 12, 2023

18 views

Show that the relation R in the set (1,2,3) given by R={(1,1),(2,2),(3,3),(1,2),(2,3)} is reflexive but neither symmetric nor transitive.

Chandan Asked Sep 12, 2023

by Chandan

1 Answer

0 Votes

18 Views

Chandan Asked Sep 12, 2023

100 views

Check whether the relation R defined in the set {1,2,3,4,5,6} as R= {(a, b) : b=a+1} is reflexive, symmetric or transitive.

Chandan Asked Sep 12, 2023

by Chandan

1 Answer

0 Votes

100 Views

Chandan Asked Sep 12, 2023

27 views

Show that the relation R in the set {1,2,3}, given by R={(1,2),(2,1)} is not reflexive.

Chandan Asked Sep 12, 2023

by Chandan

1 Answer

0 Votes

27 Views

LEELADHAR YADAV Asked Aug 22, 2023

41 views

Let $f: X \rightarrow Y$ be a function. Define a relation $R$ on $X$ given by $R=\{(a, b): f(a)=f(b)\}$. Show that $R$ is an equivalence relation on $X$.

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

41 Views

LEELADHAR YADAV Asked Aug 22, 2023

45 views

Show that the relation $S$ defined on the set $N \times N$ by $(a, b) S(c, d) \Rightarrow a+d=b+c$ is an equivalence relation.

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

45 Views

LEELADHAR YADAV Asked Aug 22, 2023

27 views

Show that the relation S in the set $A=\{x \in Z: 0 \leq x \leq 12\}$ given by $S=\{(a, b): a, b \in Z,|a-b|$ is divisible by 4$\}$ is an equivalence relation. Find the set of all elements related to 1 .

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

27 Views

LEELADHAR YADAV Asked Aug 22, 2023

30 views

Show that the relation S in the set $A=\{x \in Z: 0 \leq x \leq 12\}$ given by $S=\{(a, b): a, b \in Z,|a-b|$ is divisible by 4$\}$ is an equivalence relation. Find the set of all elements related to 1 .

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

30 Views

LEELADHAR YADAV Asked Aug 22, 2023

97 views

Show that the relation S in the set R of real numbers, defined as $S=\left\{(a, b): a, b \in R\right.$ and $\left.a \leq b^2\right\}$ is neither reflexive, nor symmetric nor transitive.

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

97 Views

LEELADHAR YADAV Asked Aug 21, 2023

35 views

Show that the relation R defined by (a, b) R(c, d) $\Rightarrow a+d=b+c$ on the set N x N is an equivalence relation.

LEELADHAR YADAV Asked Aug 21, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

35 Views

LEELADHAR YADAV Asked Aug 19, 2023

93 views

Let R be the set of real numbers. Statement-1 : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence relation on $R$. Statement-2 : $B=\{(x, y) \in R \times R: x=\alpha y$ for some rational number $\alpha\}$ is an equivalence relation on R.

LEELADHAR YADAV Asked Aug 19, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

93 Views

LEELADHAR YADAV Asked Aug 19, 2023

33 views

Define the relation R by : $R=\{(x, y) \in W \times W \mid$ the words x and y have at least one letter in common. Then R is-

LEELADHAR YADAV Asked Aug 19, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

33 Views

LEELADHAR YADAV Asked Aug 19, 2023

41 views

Let $R=\{(3,3),(6,6),(9,9),(12,12)(6,12),(3,9),(3,12),(3,6)\}$ be relation on the set $A=\{3,6,9,12\}$. Then the relation R is

LEELADHAR YADAV Asked Aug 19, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

41 Views

LEELADHAR YADAV Asked Aug 16, 2023

53 views

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

LEELADHAR YADAV Asked Aug 16, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

53 Views

LEELADHAR YADAV Asked Aug 16, 2023

128 views

Let L denote the set of all straight lines in a plane. Let a relation $R$ be defined by $\alpha R \beta \Leftrightarrow \alpha \perp \beta, \alpha, \beta \in L$. The R is

LEELADHAR YADAV Asked Aug 16, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

128 Views

LEELADHAR YADAV Asked Aug 16, 2023

48 views

Let R_1 be a relation defined by $R_1=\{(a, b) \mid a \geq b ; a, b \in R\}$. Then $R_1$ is

LEELADHAR YADAV Asked Aug 16, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

48 Views

LEELADHAR YADAV Asked Aug 15, 2023

44 views

Let A={p, q, r}. Which of the following is an equivalence relation on A?

LEELADHAR YADAV Asked Aug 15, 2023

by LEELADHAR YADAV

1 Answer

1 Vote

44 Views

LEELADHAR YADAV Asked Aug 15, 2023

42 views

The relation R defined in A={1,2,3} by a R b if $\left|a^2-b^2\right| \leq 5$. Which of the following is false :

LEELADHAR YADAV Asked Aug 15, 2023

by LEELADHAR YADAV

1 Answer

1 Vote

42 Views

LEELADHAR YADAV Asked Aug 15, 2023

103 views

Which one of the following relations on R is equivalence relation

LEELADHAR YADAV Asked Aug 15, 2023

by LEELADHAR YADAV

1 Answer

1 Vote

103 Views

LEELADHAR YADAV Asked Aug 15, 2023

115 views

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

LEELADHAR YADAV Asked Aug 15, 2023

by LEELADHAR YADAV

1 Answer

1 Vote

115 Views

LEELADHAR YADAV Asked Aug 15, 2023

58 views

In the set A={1,2,3,4,5} a relation R is defined by $R=\{(x, y) \mid x, y \in A$ and $x<y\}$. Then R is

LEELADHAR YADAV Asked Aug 15, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

58 Views

LEELADHAR YADAV Asked Aug 15, 2023

110 views

The relation R defined in N as aRbb is divisible by a is

LEELADHAR YADAV Asked Aug 15, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

110 Views

LEELADHAR YADAV Asked Aug 15, 2023

88 views

The relation "less than" in the set of natural number is

LEELADHAR YADAV Asked Aug 15, 2023

by LEELADHAR YADAV

1 Answer

1 Vote

88 Views

LEELADHAR YADAV Asked Aug 15, 2023

90 views

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

LEELADHAR YADAV Asked Aug 15, 2023

by LEELADHAR YADAV

1 Answer

1 Vote

90 Views

LEELADHAR YADAV Asked Aug 13, 2023

83 views

Consider a relation R defined on set of square matrices A of order 2 satisfying $A^2=I$. If A, B are two such matrices then relation R is defined as $(A, B) \in R \Rightarrow(A B)^{\top}=A^{\top} B^{\top}$. Prove that relation R is reflexive and symmetric.

LEELADHAR YADAV Asked Aug 13, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

83 Views

LEELADHAR YADAV Asked Aug 13, 2023

34 views

Prove that the relation $R=\left\{(x, y): x^2=x y\right\}$ is reflexive and transitive but not symmetric

LEELADHAR YADAV Asked Aug 13, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

34 Views

LEELADHAR YADAV Asked Aug 13, 2023

66 views

For n, m $\in$ N, n $\mid$ m means that n is a factor of m, then prove that relation | is reflexive, transitive but not symmetric.

LEELADHAR YADAV Asked Aug 13, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

66 Views

LEELADHAR YADAV Asked Aug 13, 2023

94 views

Let L be the set of all straight lines in the Euclidean plane. Two lines $\ell_1$ and $\ell_2$ are said to be related by the relation R if $\ell_1$ is parallel to $\ell_2$. Then prove that R is equivalence relation.

LEELADHAR YADAV Asked Aug 13, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

94 Views

LEELADHAR YADAV Asked Aug 13, 2023

107 views

Let R be a relation over the set N × N and it is defined by $(a, b) R(c, d) \Rightarrow a+d=b+c$. Then prove that R is equivalence relation

LEELADHAR YADAV Asked Aug 13, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

107 Views

LEELADHAR YADAV Asked Aug 13, 2023

76 views

Let n be a fixed positive integer. Define a relation R on the set of integers Z, $a R b \Leftrightarrow n \mid(a-b)$. Then prove that R is equivalence relation

LEELADHAR YADAV Asked Aug 13, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

76 Views

LEELADHAR YADAV Asked Aug 22, 2023

140 views

State the reason for the relation R in the set (1,2,3) given by R=(1,2),(2,1) not to be transitive.

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

140 Views

LEELADHAR YADAV Asked Aug 19, 2023

125 views

Consider the following relation R on the set of real square matrices of order 3 . $R=\left\{(A, B) \mid A=P^{-1} B P\right.$ for some invertible matrix $\left.P\right\}$.

LEELADHAR YADAV Asked Aug 19, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

125 Views

Chandan Asked Sep 12, 2023

58 views

Show that the relation R in R defined as $R=\{(a, b): a \leq b\}$ is not symmetric.

Chandan Asked Sep 12, 2023

by Chandan

1 Answer

0 Votes

58 Views

LEELADHAR YADAV Asked Aug 22, 2023

91 views

Let $Z$ be the set of all integers and R be the relation on Z defined as $R=\{(a, b): a, b \in Z$, and $(a-b)$ is divisible by 5} Prove that $R$ is an equivalence relation.

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

91 Views

LEELADHAR YADAV Asked Aug 22, 2023

65 views

Prove that the relation R in the set A=(1,2,3,4,5) given by $R=\{(a, b):|a-b|$ is even $\}$, is an equivalence relation.

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

65 Views

LEELADHAR YADAV Asked Aug 19, 2023

29 views

Let $R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}$ be a relation on the set A={1,2,3,4}. The relation R is-

LEELADHAR YADAV Asked Aug 19, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

29 Views

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What is Relation?

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