Question

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

• A. $R,S$ are transitive $\Rightarrow R\cup S$ is transitive
• B. $R,S$ are transitive $\Rightarrow R\cap S$ is transitive
• C. $R,S$ are symmetric $\Rightarrow R\cup S$ is symmetric
• D. $R,S$ are reflexive$\Rightarrow R\cap S$ is reflexive

Answer 1

The correct option is A

$R,S$ are transitive $\Rightarrow R\cup S$ is transitive

Explanation for the correct option:

Let A$=\{1,2,3\}$, and

let R$=\left\{\right(1,1),(1,2)\}$
S $=\left\{\right(2,2),(2,3)\}$ be transitive relation on A.
Then,

R$\cup$S$=\left\{(1,1),(1,2),(2,2),(2,3)\right\}$
R$\cup$S is not transitive, since $(1,2)\in$R$\cup$S and
$(2,3)\in$R$\cup$S but $(1,3)$ does not belong to R$\cup$S.

Hence, option(A) is the correct answer