Suppose E is the set of well-formed algebraic expressions, with vr(e) and op(e) denoting the number of variables and operator occurrences in an expression e∈E.

1)

Expressions in E use infix notation because each operator is placed in between the operands it acts on. Another way to write these expressions is to use postfix notation, where each operator is placed after the operands it acts on. For example the expression

(((x+x)-(x/y))+z), written using postfix notation would be

xx+xy/-x+

(Note the parentheses are not needed for the postfix notation). Use structural induction to define the set EP of well-formed algebraic expressions in postfix notation.

2)

Use structural induction to prove that for any nonempty prefix u of an expression e∈EP, vr(u)>op(u).

How do I begin these questions? I'm not really sure what they are asking...