Answer the following questions
1. Prove that the algorithm shown in Figure 19.4 correctly computes the attribute closure of the input attribute set X.
2. Describe a linear-time (in the size of the set of FDs, where the size of each FD is the number of attributes involved) algorithm for finding the attribute closure of a set of attributes with respect to a set of FDs. Prove that your algorithm correctly computes the attribute closure of the input attribute set.