State True or False with reason. There is always a decomposition into Boyce-codd normal form $$(BCNF)$$ that is lossless and dependency preserving.

Give a relational algebra expression using only the minimum number of operators from $$\left( { \cup ,\, - } \right)$$ which is equivalent to $$R \cap S$$.

An instance of a relational scheme R(A, B, C) has distinct values for attribute A. Can you conclude that A is a candidate key for R?

Let $$p$$ and $$q$$ be propositions. Using only the truth table decide whether $$p \Leftrightarrow q$$ does not imply $$p \to \sim q$$ is true or false.