Discuss the validity of the following statements. What is more important than whether you ultimately classify the statement as true or false is your justification for arriving at your conclusion.

1. A scanner must always discard whitespace and comments.

2. For an unambiguous grammar, the parse trees corresponding to a leftmost derivation of a sentence will be the same as the parse tree corresponding to a rightmost derivation of the same sentence.

3. It is possible to write arithmetic expressions without needing to use grouping parentheses.

4. In a modern language which allowed a prefix * operator and infix * and ** operators, the expression a**b would be interpreted as a*(*b).

5. Denotational semantics is a popular way of describing the semantics of programming languages.