recursive definition help

[bladeb2k]

basically this is 2 questions i have to do which is the final part of a paper that started with me having to design a turing machine that checks that strings of binary digits are formatted correctly with { and } formatted correctly. ie
10 {100 } 1 is ok but }101{1} is not.



4. Assuming that the meaning of ?number? in the above grammar is understood complete the following recursive definition of valid input by filling in the blanks.
1. A number is a valid input
2. If X is a valid input so is ---------------
3. If X and Y are valid inputs so is ------------------
4. These represent all legal inputs.
Using these definition show that the following are legal inputs
a) 1, {1}
b) {1,{1}}
c) 1
Is {} a legal input according to this definition? Justify your answer.
25 marks