(a) Consider the relation scheme $$R(A, B, C)$$ with the following functional dependencies:
$$\eqalign{ & A,B \to C \cr & \,\,\,\,\,\,C \to A \cr} $$
Show that the scheme $$R$$ is the Third Normal Form $$(3NF)$$ but not in Boyce-Code Normal Form $$(BCNF).$$

(b) Determine the minimal keys of relation $$R.$$

If the proposition $$\neg p \Rightarrow q$$ is true, then the truth value of the proposition $$\neg p \vee \left( {p \Rightarrow q} \right)$$ where $$'\neg '$$ is negation, $$' \vee '$$ is inclusive or and $$' \Rightarrow '$$ is implication, is

A bag contains 10 white balls and 15 black balls. Two balls drawn in succession. The probability that one of them is black the other is white is

Let A be the set of all nonsingular matrices over real numbers and let * be the matrix multiplication operator. Then