3 Problem-Derivation, Parse Tree, Ambiguity, Prece- dence & Associativity A language that is a subset of the language of propositional logic may be defined as follows: :- ::-true | false 1. Give a leftmost and a rightmost derivation for the sentence a true b-false v true 2. Give the corresponding parse trees for the derivations. 3. Give the corresponding abstract syntax tree (AST). 4. Show that the above grammar is ambiguous. 5. Give an unambiguous grammar for the same language that enforces the following prece- ence and associativity: has highest precedence (binds strongest), followed by V. and then ^ is right associative, and and V are left associative 6. Give the parse tree and AST for your new, unambiguous grammar for the sentence a false b true