Let R(A,B,C,D,E) be a relation schema, and let F = {A BC, CD E, BD,EA} be a set of functional dependencies (FDs). Show for each of the following FDs whether they can be logically implied from F by using Armstrong's axioms and their derived inference rules. Show each step. (1) [3 points] BC AE (2) [3 points] A E Let R(A,B,C,D,E,F) be a relation schema, and let F = {AB E,AC F,BEF D} be a set of functional dependencies (FDs). Which of the following attribute sets is a candidate key? Explain your answer by using Armstrong's axioms and their derived inference rules. BEF ABC DE Let R(A,B,C,D,E,F) be a relation schema, and let F = {AB C,BC DE,AC E,DEF} be a set of functional dependencies (FDs). Infer at least five new FDs by using Arm- strong's axioms and their derived inference rules. All rules in your answer should be different.