Give a CFG for valid regular expressions over the alphabet Σ = {a,b}. The alphabet of your grammar should be over {a, b, (, ), U,*, A, Ø}. You may insert more parenthesis than necessary. Here we shall use A to represent the base-case regular expression symbolizing the set only containing the empty string. Use & not as part of the regular expression, but if necessary, as part of the rules of the grammar to satisfy (VUΣ)*. You must generate all syntactically valid regular expressions.

d. Write a Lisp program that verifies if a list of symbols is correct from the point of view of this grammar. For example, (check-A '(y w z w y)) (check-A '(y z w w)) should return true (t) and should return false (nil).

Develop a system/application in Prolog that will allow grader to: load a set of student’s grades (see samples from the Table C below) query student’s final letter grade (A, B, C, etc.) by a given student’s name. query student(s) whose grade matches to the input letter grade (e.g., A). For example, show student(s) whose final letter grade is A. There are 3 types of grades for each student—HWs, Exams, and Project, with a weight of 20%, 40% and 40%, respectively, to the 100-point final. Table A and B show how the final grades (in points and letter) are computed. Table C shows samples of students’ grades. You will define the execution instructions to answer the following questions so that grader can test out your application in Prolog: how to load your source code to Prolog runtime/compiler how to load students’ grades to Prolog runtime/compiler how to query student’s letter grade how to query student(s) whose letter grade matches to an input letter grade Please DO NOT hard code any…

I always get the wrong answer for these three, can you please provide me the correct answer for First(S') First(A) (Please see the picture as well)