solve 8 questions relate to database Systems

Other 4 in the attachments: 1. Consider relation R = ABCDE with FDs AB→C, CD→E, and DE→A. Convert this to BCNF. 2. Let R be a relation, X a set of attributes of R, and A an attribute of R. (Also, denote by XA the result of adding A to X.) Define the support of X, written #X, as the number of distinct tuples in R|X (R restricted to, or projected onto, the attributes of X). Prove that if X→A, then #X=#XA. 3. Insert the following values into an initially empty B+ tree with parameter n=4: 17, 11, 50, 22, 5, 35, 42, 60, 15, 30, 25, 27, 37, 40, 20. 4. Repeat the previous problem for parameter n=3.