Let A = {1, 2, 3, 4} and R = {(1, 2), (2, 3), | vedclass

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

Question

(A) An equivalence relation $S$ must be reflexive,symmetric,and transitive.Given $R = \{(1, 2), (2, 3), (1, 4)\}$.$1$. Reflexivity: $S$ must contain $

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(A) An equivalence relation $S$ must be reflexive,symmetric,and transitive.Given $R = \{(1, 2), (2, 3), (1, 4)\}$.$1$. Reflexivity: $S$ must contain $(1, 1), (2, 2), (3, 3), (4, 4)$.$2$. Symmetry: Since $(1, 2) \in S$,then $(2, 1) \in S$. Since $(2, 3) \in S$,then $(3, 2) \in S$. Since $(1, 4) \in S$,then $(4, 1) \in S$.$3$. Transitivity: Since $(1, 2) \in S$ and $(2, 3) \in S$,then $(1, 3) \in S$. By symmetry,$(3, 1) \in S$.Since $(1, 3) \in S$ and $(3, 2) \in S$,we already have $(1, 2) \in S$.Since $(1, 4) \in S$ and $(4, 1) \in S$,we have $(1, 1) \in S$ (already included).Since $(2, 3) \in S$ and $(3, 2) \in S$,we have $(2, 2) \in S$ (already included).Since $(1, 2) \in S$ and $(2, 1) \in S$,we have $(1, 1) \in S$.Checking the equivalence classes: $1$ is related to $2, 3, 4$. Thus,$1, 2, 3, 4$ are all in the same equivalence class.If all elements are in one equivalence class,$S = A 	imes A$.The number of elements $n = 4 	imes 4 = 16$.

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:

Similar Questions

In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation,it is sufficient,if $R$

The relation "is subset of" on the power set $P(A)$ of a set $A$ is

Determine whether the following relation is reflexive,symmetric,and transitive:
Relation $R$ in the set $A$ of human beings in a town at a particular time given by $R = \{(x, y): x \text{ and } y \text{ work at the same place}\}$.

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

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module