Consider a digraph G = (V, E) with at least two nodes. Prove that the following...

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Consider a digraph G = (V, E) with at least two nodes. Prove that the following statements are equivalent: (i) G has a globally reachable node, and (ii) for every pair S₁, S₂ of non-empty disjoint subsets of V, there exists a node that is an out-neighbor of S₁ or S₂. Hint: Use induction on the number of nodes in V. Please use clear and readable handwriting Consider a digraph G = (V, E) with at least two nodes. Prove that the following statements are equivalent: (i) G has a globally reachable node, and (ii) for every pair S₁, S₂ of non-empty disjoint subsets of V, there exists a node that is an out-neighbor of S₁ or S₂. Hint: Use induction on the number of nodes in V. Please use clear and readable handwriting

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