Question

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

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

Answer 1

Answer: (D)

$R$ and $S$ are reflexive $\Rightarrow R \cap S$ is reflexive

Answer 2

Answer (d) $R$ and $S$ are reflexive $\Rightarrow R \cap S$ is reflexive