In a compact single dimensional array representation for lower triangular matrices (i.e all the elements above the diagonal are zero) of size n $$\times$$ n, non-zero elements (i.e., elements of the lower triangle) of each row are stored one after another, starting from the first row, the index of the (i, j)^th element of the lower triangular matrix in this new representation is

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?

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

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