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

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LEELADHAR YADAV Asked Aug 22, 2023

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Chandan Asked Sep 12, 2023

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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.

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Chandan Asked Sep 12, 2023

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

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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.

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LEELADHAR YADAV Asked Aug 22, 2023

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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

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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

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LEELADHAR YADAV Asked Aug 15, 2023

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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

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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

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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

by LEELADHAR YADAV

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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 19, 2023

30 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

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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 19, 2023

137 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

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LEELADHAR YADAV Asked Aug 15, 2023

44 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

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1 Vote

44 Views

LEELADHAR YADAV Asked Aug 16, 2023

136 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

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LEELADHAR YADAV Asked Aug 15, 2023

93 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

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1 Vote

93 Views

LEELADHAR YADAV Asked Aug 13, 2023

34 views

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

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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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98 Views

LEELADHAR YADAV Asked Aug 19, 2023

43 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

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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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Chandan Asked Sep 12, 2023

25 views

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 13, 2023

55 views

Let $R=\{(x, y): x, y \in A, x+y=5\}$ where A={1,2,3,4,5} then prove that R is neither reflexive nor transitive but symmetric.

LEELADHAR YADAV Asked Aug 13, 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=

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by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 13, 2023

36 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

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LEELADHAR YADAV Asked Aug 11, 2023

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Given a binary operation $: A \times A \rightarrow A$ with the identity element $e$ in $A$, an element $a \in A$ is said to be invertible with respect to the operation * if there exists an element $b$ in A such that $a^* b=e=b^* a$ and $b$ is called the inverse of $a$ and is denoted by ${a}^{-1}$.

LEELADHAR YADAV Asked Aug 11, 2023

by LEELADHAR YADAV

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93 Views

LEELADHAR YADAV Asked Aug 13, 2023

70 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

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LEELADHAR YADAV Asked Aug 11, 2023

35 views

Show that " : $R \times R \rightarrow R$ given by a " $b \rightarrow a+2 b$ is not associative.

LEELADHAR YADAV Asked Aug 11, 2023

by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 13, 2023

90 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

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0 Votes

90 Views

LEELADHAR YADAV Asked Aug 13, 2023

83 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

83 Views

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

1 Answer

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LEELADHAR YADAV Asked Aug 21, 2023

36 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

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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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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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LEELADHAR YADAV Asked Aug 22, 2023

39 views

Consider the binary operation * on the set $\{1,2,3,4,5\}$ defined by $a^* b=\min \{a, b\}$. Write the operation table of the operation *.

LEELADHAR YADAV Asked Aug 22, 2023

by LEELADHAR YADAV

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LEELADHAR YADAV Asked Aug 13, 2023

99 views

Let * be a binary operation on Z × Z defined by $(a, b)^*(c, d)=(a+c, b+d) ;(a, b),(c, d) \in Z \times Z$. Find $(1,2) *(3,5)$ and $(4,3) *(1,0)$.

LEELADHAR YADAV Asked Aug 13, 2023

by LEELADHAR YADAV

1 Answer

0 Votes

99 Views

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

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