7. Design a CFG that generates the arithmetic expressions, with t, -, *, (), a, b, c, together with a new terminal symbol for exponentiation t. Your grammar should be unambiguous, properly associative. More specifically, it should be left associative for addition +, - and multiplication*, right associative for the exponentiation t. (Recall that, being left associa- tive for addition , an expression such as a +b+c should have the unique arsing as the sum of a + b and c.) It should also have a precedence rule embedded in the grammar that is highest for exponentiation, second high- est for multiplication, and finally for addition/subtraction. With addition and subtraction, whichever is left most gets precedence. For example: for the expression The only valid derivation should parse it as such: First, f t g, then etft g: also, c"d, then cd etftg: also a + b and then a + b- .. (You-don't need to prove all the requirements here are satisfied. But if you correctly prove that all the requirements here are satisfied, you will earn extra credit.)