$($a$)$ Describe Warshall's algorithm for the sequences of the matrices $W_k=[w_{ij}^{[k]}]$ with kin$\{1,2,$dots,$n\}$ in terms of pseudocode.

$($b$)$ Show that Warshall's algorithm requires $2n^3$ bits operations to compute $W_n=M_{R^{**}}$ from the input $W=M_R$

$($c$)$ Let $R$ be the relation defined on a set $A=\{a,b,c,d,e\}$ by

$R=\{(a,c),(b,d),(c,a),(d,b),(e,d)\}$

Use Warshall's algorithm to find the transitive closures of $R.$