Q3Multiple correct4 Marks22 Dec 2024

Devendra has three sons (Jatin, Rabi, and Hem). Rabi has one son named Rathi. Hem has two sons (Avi and Manish). This family tree has been shown in the figure below. Let us define relations $R$ and $S$ as follows: - $R := \{(A, B) \mid A \text{ and } B \text{ are first cousins, i.e., their parents are siblings}\}$ - $S := \{(A, B) \mid A \text{ is the son of } B\}$ Which of the following is (are) true?

A

$R$ is an equivalence relation.

B

$(\text{Rathi}, \text{Rabi}) \in S$ but $(\text{Rabi}, \text{Rathi}) \notin S$.

C

$(\text{Rathi}, \text{Hem}) \in R$.

D

$(\text{Jatin}, \text{Devendra}) \in S$ but $(\text{Rathi}, \text{Devendra}) \notin S$.