Ithinkthe first thing to do comes as to write out exactly E in infix notation gets defined. It probably goes something like this:

1) Every algebraic variable and constant a, b, c, ..., z qualifies as a well-formed expression.

2) If x comes as well-formed, then ~x comes as well-formed where ~ indicates a unary operator (or operation).

3) If x and y come as well-formed, then (x*y) comes as well-formed where * indicates a binary operator.

4) No other expressions come as well-formed (in this notation).

Then for prefix and postfix notation, you'll need to rewrite that definition in appropriate terms. This just means changing ~x to ~x, or x~ as needed, and (x*y) to *xy or xy* as needed. I think that's all you have to do for the first question, since it doesn't ask for a proof by structural induction, just a definition, though I'M NOT SURE.

Given that the constants or variables get defined as well-formed algebraic expression the second question isn't quite right. For every expression Nx where x indicates a constant or variable, and "N" a unary operator, we have vr(u)=op(u). So, it should go vr(u) (u). The base case here will consist of showing this holds for every algebraic variable or constant. Then you'll need that given that for every recursive rule from x_1, ..., x_n to x, that if vr(x_1) (x_1), vr(x_2) op(x_2)..., vr(x_n) op(x_n). This might help here Structural Induction

I'd like to know what you come up with here!