In a directed graph define two functions:
\( f(u, v) \): there exists a directed path from \(u\) to \(v\) .
\( scc(u) \) : Returns the SCC containing node \(u\).
For each of the following logical statements, determine whether it is True or False for any arbitrary directed graph:
- \( scc(u) = scc(v) \Longrightarrow f(u,v) \)
- \( (f(u,v) \) and \( f(v,u)) \Longleftrightarrow scc(u) = scc(v) \)
- \( f(u,v) \Longrightarrow scc(u) = scc(v) \)
- \( (f(u,v) \) and \( f(v,w)) \Longrightarrow f(u,w) \)
Alternatives
a) TTFT
b) TFFF
c) TFFT
d) TTTT
e) None of the above
Original idea by: Luis Alberto Vásquez Vargas
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