On set A = {1, 2, 3}, relations R and S are g | vedclass

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

Question

(C) Given $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)\}$ and $S = \{(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)\}$.$R \cup S = \{(1, 1), (2, 2), (3, 3),

Vedclass · Accepted Answer

$R \cup S$ is reflexive and symmetric but not transitive

Vedclass · Answer

(C) Given $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)\}$ and $S = \{(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)\}$.$R \cup S = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (1, 3), (3, 1)\}$.$1$. Reflexivity: Since $(1, 1), (2, 2), (3, 3) \in R \cup S$, it is reflexive.$2$. Symmetry: Since $(1, 2) \in R \cup S \implies (2, 1) \in R \cup S$ and $(1, 3) \in R \cup S \implies (3, 1) \in R \cup S$, it is symmetric.$3$. Transitivity: We have $(2, 1) \in R \cup S$ and $(1, 3) \in R \cup S$. If it were transitive, $(2, 3)$ must be in $R \cup S$. However, $(2, 3) 
otin R \cup S$. Thus, it is not transitive.Therefore, $R \cup S$ is reflexive and symmetric but not transitive.

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,

Similar Questions

In the set of all $3 \times 3$ real matrices, a relation is defined as follows: $A$ matrix $A$ is related to a matrix $B$ if and only if there exists a non-singular $3 \times 3$ matrix $P$ such that $B = P^{-1} A P$. This relation is

Let $R$ be a relation defined on the set $\{1,2,3,4\} \times \{1,2,3,4\}$ by $R = \{((a,b), (c,d)) : 2a + 3b = 3c + 4d\}$. Then the number of elements in $R$ is:

If $R = \{(6, 6), (9, 9), (6, 12), (12, 12), (12, 6)\}$ is a relation on set $A = \{3, 6, 9, 12\}$,then relation $R$ is

Consider the following two binary relations on the set $A = \{a, b, c\}$: $R_1 = \{(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)\}$ and $R_2 = \{(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)\}$. Then

Let $N$ be the set of natural numbers and the relation $R$ on $N \times N$ is defined by $(a, b) R (c, d)$ if $ad(b + c) = bc(a + d)$. Then $R$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module