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

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LEELADHAR YADAV Asked Aug 16, 2023

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LEELADHAR YADAV Asked Aug 13, 2023

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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

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LEELADHAR YADAV Asked Aug 22, 2023

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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

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LEELADHAR YADAV Asked Aug 16, 2023

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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

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LEELADHAR YADAV Asked Aug 19, 2023

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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

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LEELADHAR YADAV Asked Aug 13, 2023

81 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

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LEELADHAR YADAV Asked Aug 13, 2023

110 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

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LEELADHAR YADAV Asked Aug 16, 2023

51 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

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LEELADHAR YADAV Asked Aug 15, 2023

61 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

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LEELADHAR YADAV Asked Aug 13, 2023

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Let * be a binary operation on the set R defined by $a{ }^* b=a+b+a b, a, b \in R$. Solve the equation $2^*\left(3^{\star} x\right)=7$

LEELADHAR YADAV Asked Aug 13, 2023

by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 22, 2023

100 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

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LEELADHAR YADAV Asked Aug 21, 2023

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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

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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

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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

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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

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LEELADHAR YADAV Asked Aug 13, 2023

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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

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LEELADHAR YADAV Asked Aug 19, 2023

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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

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LEELADHAR YADAV Asked Aug 15, 2023

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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

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LEELADHAR YADAV Asked Aug 19, 2023

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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

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LEELADHAR YADAV Asked Aug 16, 2023

57 views

Let S be the set of all real numbers. Then the relation R $\{(a, b): 1+a b>0\}$ on S is

LEELADHAR YADAV Asked Aug 16, 2023

by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 17, 2023

79 views

Let * be a binary operation on Z defined by $x^* y=x^2+y^2+x y ; x, y \in Z$. The value of $\left[\left(1^* 2\right)+\left(0^* 3\right)\right]^2$ is

LEELADHAR YADAV Asked Aug 17, 2023

by LEELADHAR YADAV

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Chandan Asked Sep 12, 2023

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Is the binary operation * defined on set N, given by $a * b=\frac{a+b}{2}$ for all $a, b \in Q$, commutative?

Chandan Asked Sep 12, 2023

by Chandan

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LEELADHAR YADAV Asked Aug 19, 2023

52 views

Let R be the real line. Consider the following subsets of the plane R×R $S=\{(x, y): y=x+1 \text { and } 0<x<2\} \\ T=\{(x, y): x-y \text { is an integer }\}$

LEELADHAR YADAV Asked Aug 19, 2023

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LEELADHAR YADAV Asked Aug 22, 2023

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Let * be a binary operation on set of integers $I$, defined by $a{ }^* b=2 a+b-3$. Find the value of $3 * 4$

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

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51 Views

LEELADHAR YADAV Asked Aug 17, 2023

38 views

Let * be a binary operation on $\mathrm{N}$ defined by $\mathrm{a}^* \mathrm{~b}=2^{5 \mathrm{ab}} ; \mathrm{a}, \mathrm{b} \in \mathrm{N}$. then the binary operation * is

LEELADHAR YADAV Asked Aug 17, 2023

by LEELADHAR YADAV

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Chandan Asked Sep 12, 2023

104 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

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104 Views

LEELADHAR YADAV Asked Aug 22, 2023

65 views

Let " be a binary operation on set Q of rational numbers defined as $a$ * $b=\frac{a b}{5}$. Write the identity for ", if any

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 17, 2023

141 views

Let A={1,2,3,4,5,6} and * be an operation A defined by $a{ }^* b=r$, where r is the least non-negative remainder when the product a b is divided by k. Operation * is binary operation if k=

LEELADHAR YADAV Asked Aug 17, 2023

by LEELADHAR YADAV

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0 Votes

141 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

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0 Votes

45 Views

LEELADHAR YADAV Asked Aug 22, 2023

66 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

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66 Views

LEELADHAR YADAV Asked Aug 17, 2023

105 views

Let * be a binary operation on Z defined by a * b=a+b−15 . The inverse of element 21 in Z, ) is

LEELADHAR YADAV Asked Aug 17, 2023

by LEELADHAR YADAV

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105 Views

LEELADHAR YADAV Asked Aug 13, 2023

82 views

Let A be the set of all subsets of a non-empty set S. Show that the binary operation 'union' on A is left distributive over the binary operation 'intersection' on A. Also show that 'intersection' is left distributive over 'union'.

LEELADHAR YADAV Asked Aug 13, 2023

by LEELADHAR YADAV

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82 Views

LEELADHAR YADAV Asked Aug 22, 2023

142 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

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0 Votes

142 Views

Chandan Asked Sep 12, 2023

39 views

Is * defined on the set {1,2,3,4,5} by a*b = l.c.m. of a and b binary operation?

Chandan Asked Sep 12, 2023

by Chandan

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39 Views

LEELADHAR YADAV Asked Aug 15, 2023

116 views

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

LEELADHAR YADAV Asked Aug 15, 2023

by LEELADHAR YADAV

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116 Views

LEELADHAR YADAV Asked Aug 22, 2023

110 views

Consider the binary operations $*: R \times R \rightarrow R$ and $o: *: R \times R \rightarrow R$ defined as $a * b=|a-b|$ and $a \circ b=a$ for all $a, b \in R$. Show that ' $x$ ' is commutative but not associative ' $o$ ' is associative but not commutative.

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

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1 Vote

110 Views

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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

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