The following ambiguous grammar describes boolean expressions: B → true B → false B → B ∨ B B → B ∧ B B → ¬ B B → (B) a) Given that negation (¬) binds tighter than conjunction (∧) which binds tighter...

The following ambiguous grammar describes boolean expressions:

B → true

B → false

B → B ∨ B

B → B ∧ B

B → ¬ B

B → (B)

a) Given that negation (¬) binds tighter than conjunction (∧) which binds tighter

than disjunction (∨) and that conjunction and disjunction are both rightassociative, rewrite the grammar to be unambiguous.

b) Write a grammar that accepts the subset of boolean expressions that are equivalent to true (i.e., tautologies). Hint: Modify the answer from question a) and add

an additional nonterminal F for false boolean expressions.