12. For each of the following problems, state whether it is in NP, co-NP, or both. Justify your answer by describing the appropriate type of witness. Example: SAT is in NP. Witness: a truth assignment x1, , an that makes the given formula evaluate to TRUE (a) 3-Coloring (b) Vertex Cover (c) Primes (d) 2-Coloring 12. For each of the following problems, state whether it is in NP, co-NP, or both. Justify your answer by describing the appropriate type of witness. Example: SAT is in NP. Witness: a truth assignment x1, , an that makes the given formula evaluate to TRUE (a) 3-Coloring (b) Vertex Cover (c) Primes (d) 2-Coloring