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Problem . Given the formula f- construct a graph G such that f is satisfiable iff G has a clique of size 3. .

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Answer #1

If x1 = True, x2 = False, x3 = True, x4 = True then:

f = (x1 \lor x2)\land (\neg x1 \lor \neg x2)\land (x3 \lor x4) = (T \lor F)\land (\neg T \lor \neg F)\land (T \lor T) = T

Thus, f is satisfiable.

So, we must construct a graph G which has a clique of size 3, because then only the "if and only if"statement would be true.

Note that if f hasn't been satisfiable then we would rather have drawn graph G which didn't have a clique of size 3, because then only the "iff" statement have been satisfiable.

Thus, our G can be simply a triangle then, because it's a clique of size three.

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