Exercise 4 (Relational Algebra) [28 points) The following questions let you think deeper about the concepts of the Relational Algebra. 1. [6 points) Let R be the schema of a relation R, and let A1, A2, ..., An C R. Is the term TIA, (TA(...(Tt4,(R))...)) = TA,(R) correct, in general? If yes, argue why. If not, argue why not. If your answer is no, are there any restrictions that could make the statement true? If so, what are these restrictions in mathematical notation? 2. [6 points) Let R be the schema of a relation R, and let A CR. What is the condition in mathematical notation such that (HR))=GHT(R)) holds where F is assumed to be a correct predicate on R? 3. [16 points) Let R(A, B) be a relation with r>0 tuples, and let S(B, C) be a relation with s> 0 tuples. We assume that A, B, and C have the same data type. For each of the following Relational Algebra expressions, in terms of r and s, determine the minimum and maximum mumber of tuples that the result relation can have. In other words, we are interested in the number of tuples the following Relational Algebra expressions can have at least and at most. The numbers have to be given by using the two variables r and s. Please note that you have to give precise explanations for your answers. a. [4 points) RUPA.B)(S) b. [3 points) ( R R) DR c. [4 points) TARS) d. [5 points] 04-CRMS)