Question: Given a graph G = (V, E) and a subset S V, show that the following three statements are equivalent: 1. S is an independent

Given a graph G = (V, E) and a subset S V, show that the following three statements are equivalent:

1. S is an independent set.

2. V - S is a vertex cover

3. S is a clique in the complemented graph show that the following three statements are equivalent: 1. S is an = (V, independent set. 2. V - S is a vertex cover 3. S ), where two vertices are adjacent if and only if they are not adjacent in G.

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