Assuming you have a class named Rational where each object contains two ints representing the numerator and the denominator, write the class definition line if you wanted to indicate that it would implement the generic interface Comparable and write the body of the required method with the signature: public boolean equals(Object other); so that it will only return true if the numerators and denominators are the same in both.

Suppose there is a relation r(a, b, c) with a b+-tree index with search keys (a, b).1. what is the worst-case cost of finding records satisfying 10 < a < 50 using this index, in terms of the number of records n1, retrieved and the height h of the tree? 2. what is the worst-case cost of finding records satisfying 10 < a < 50 and 5 < b < 10 using this index, in terms of the number of records n2 that satisfy this selection, as well as n1 and h defined above? 3. under what conditions on n1 and n2, would the index be an efficient way of finding records satisfying the condition from part (2)?