Problem $1(25$ points$)$

Consider a binary relation $R$ defined on $P(S)($i$.$e$.,$ the power set $S),$ where $S=\{1,2,3\},$ as follows:

For any ainP$(S),$binP$(S),$aRb if and only if $b=a\{2\}$

In each proof given as an answer below, you must refer explicitly to the formal definition of the property.

a$.$ Is $R$ reflexive?

First state vour answer $($YFS or NO$)$ and then nrove it in this hox

$|$ First. state vour answer $($YES or NO$)$ and then nrove it$.$ in this hox.