Q$1)[25$ points$][$ Check ch$-9$ slides$]$

Consider the following relations on $\{1,2,3\}.$

$R1=\{(1,1),(1,2),(1,3),(2,2),(2,3),(3,3)\}$

$R2=\{(x,y)|x+y4\}$

$($a$)$ What is R$2?$

$R2=$

$($b$)$ Which of these relations are reflexive $($circle$)?$ Justify your answers. R$1$: yes$/$no: Justification:

R$2$: yes$/$ no: Justification:

$($c$)$ Which of these relations are symmetric? Justify your answers. R$1$: yes$/$ no : Justification:

R$2$: yes$/$ no: Justification:

$($d$)$ Which of these relations are antisymmetric? Justify your answers. R$1$: yes$/$no: Justification: