Let H be the set of all houses in a village w | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) relation $R$ is an equivalence relation if it is reflexive,symmetric,and transitive.$1$. Reflexivity: For any house $x \in H$,$x$ faces the same d

Vedclass · Accepted Answer

an equivalence relation

Vedclass · Answer

(D) relation $R$ is an equivalence relation if it is reflexive,symmetric,and transitive.$1$. Reflexivity: For any house $x \in H$,$x$ faces the same direction as itself. Thus,$(x, x) \in R$ for all $x \in H$. So,$R$ is reflexive.$2$. Symmetry: If $(x, y) \in R$,then $x$ and $y$ face the same direction. This implies that $y$ and $x$ also face the same direction. Thus,$(y, x) \in R$. So,$R$ is symmetric.$3$. Transitivity: If $(x, y) \in R$ and $(y, z) \in R$,then $x$ and $y$ face the same direction,and $y$ and $z$ face the same direction. This implies that $x$ and $z$ face the same direction. Thus,$(x, z) \in R$. So,$R$ is transitive.Since $R$ is reflexive,symmetric,and transitive,it is an equivalence relation.

Let $H$ be the set of all houses in a village where each house is faced in one of the directions,East,West,North,South. Let $R = \{ (x,y) | (x,y) \in H \times H \text{ and } x, y \text{ are faced in same direction} \}$. Then the relation $R$ is

Similar Questions

Let $R$ be a relation on the set $A$ of ordered pairs of positive integers defined by $(x, y) R (u, v)$ if and only if $xv = yu$. Show that $R$ is an equivalence relation.

Let $A = \{1, 2, 3, 4\}$ and $R = \{(1, 2), (2, 3), (1, 4)\}$ be a relation on $A$. Let $S$ be the smallest equivalence relation on $A$ such that $R \subset S$. If the number of elements in $S$ is $n$,then the value of $n$ is:

Let $A = \{1, 2, 3, \ldots, 20\}$. Let $R_1$ and $R_2$ be two relations on $A$ such that $R_1 = \{(a, b) : b \text{ is divisible by } a\}$ and $R_2 = \{(a, b) : a \text{ is an integral multiple of } b\}$. Then,the number of elements in $R_1 - R_2$ is equal to . . . . . . .

Let $A$ be a set consisting of $10$ elements. The number of non-empty relations from $A$ to $A$ that are reflexive but not symmetric is

Determine whether the following relation $R$ in the set $A = \{1, 2, 3, 4, 5, 6\}$ defined by $R = \{(x, y) : y \text{ is divisible by } x\}$ is reflexive,symmetric,and transitive.

Vedclass Test Series

Exam Paper Generator

Online Exam Module