$($a$)$ L $R$ your own hand$-$writing$)$

$($a$)$ Let $R$ and $S$ be binary relations defined from the set $A=\{1,2,4\}$ to the set $B=\{2,6,8,10\}$ such that $(a,b)inR$ if and only if a divides $b$; and $(a,b)inS$ if and only if $b-4=a.$ List the elements of $RS,$ and $RS.\%$

$(2$ marks$)$

$($b$)$ Using Warshall's algorithm, find the transitive closure of the relation on $A=\{2,3,4,5\}$ represented by the adjacency matrix

$W_0=\{\begin{array}{c}\text{:}[2]\\ 3\\ 4\\ 5\end{array}\left[\begin{array}{cccc}2& 3& 4& 5\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\\ 0& 1& 0& 0\end{array}\right]$

$(3$ marks$)$