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

The relation $R = \{(a, a), (b, b), (c, c), (a, b), (b, a)\}$ is defined on the set $A = \{a, b, c\}$. Then $R$ is . . . . . . .

On the set of all real numbers,a relation $R$ is defined as $a \, R \, b$ if and only if $|a - b| \le 1$. Then $R$ is:

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

On set $A = \{1, 2, 3\}$, relations $R$ and $S$ are given by $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)\}$ and $S = \{(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)\}$. Then,

The relation "congruence modulo $m$" is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module