Let R and S be two non-void relations on a se | vedclass

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

Question

(a) Let $A = \{ 1,\,2,\,3\} $ and $R = \{(1, 1), (1, 2)\}, S = \{(2, 2) (2, 3)\}$ be transitive relations on $A$.

Then $R \cup S = \{(1, 1); (1, 2)

Vedclass · Accepted Answer

$R$ and $S$ are transitive ==> $R \cup S$ is transitive

Vedclass · Answer

(a) Let $A = \{ 1,\,2,\,3\} $ and $R = \{(1, 1), (1, 2)\}, S = \{(2, 2) (2, 3)\}$ be transitive relations on $A$.

Then $R \cup S = \{(1, 1); (1, 2); (2, 2); (2, 3)\}$

Obviously, $R \cup S$ is not transitive. Since $(1, 2)$ $ \in $ $R \cup S$ and $(2,\,3) \in R \cup S$ but $(1, 3)$ $ 
otin R \cup S$.

Let $R$ and $S$ be two non-void relations on a set $A$. Which of the following statements is false

Similar Questions

Show that the relation $R$ in the set $A$ of all the books in a library of a college, given by $R =\{(x, y): x $ and $y$ have same number of pages $\}$ is an equivalence relation.

If $R \subset A \times B$ and $S \subset B \times C\,$ be two relations, then ${(SoR)^{ - 1}} = $

Check whether the relation $R$ in $R$ defined by $S =\left\{(a, b): a \leq b^{3}\right\}$ is reflexive, symmetric or transitive.

Let $A=\{1,2,3\} .$ Then number of equivalence relations containing $(1,2)$ is

Show that the number of equivalence relation in the set $\{1,2,3\} $ containing $(1,2)$ and $(2,1)$ is two.