$($b$)$ How many cards must you draw from a standard $52-$card deck to ensure that you have two cards of the same denomination?P

$($c$)$ Define the relation $$ on $N$ by $ab$ if $b2a.$

i$.$ Provide three specific examples of elements a and $b$ in $N$ so that $ab.$

ii$.$ Provide three specific examples of elements a and $b$ in $N$ so that $ab.$