How many undirected graphs (not necessarily connected) can be constructed out of a given set V = { v₁,v₂,........,v_n } of n vertices?

Consider a schema $$R(A,B,C,D)$$ and functional dependencies $$A \to B\,\,$$ and $$C \to D\,\,$$. Then the decomposition of $$R$$ into $${R_1}\left( {AB} \right)$$ and $${R_2}\left( {CD} \right)$$ is

$$R(A,B,C,D)$$ is a relation. Which of the following does not have a lossless-join, dependency preserving $$BCNF$$ decomposition?

Which of the following relational calculus expressions is not safe?