Please answer all questions

A language that is a subset of the language of propositional logic may be defined as follows: ::=::=::=::=truefalseabc 1. Give a leftmost and a rightmost derivation for the sentence atruebfalsetrue. 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 precedence and associativity: - has highest precedence (binds strongest), followed by , and then - is left associative, and and are right associative 6. Give the parse tree and AST for your new, unambiguous grammar for the sentence a true b false