Precedence rules of the operators

Question

1. For the given formula (!d|b->a) & a , after applying the precedence rule it should be written as ((!d|b)->a) & a but not (!d|(b->a)) & a Is it correct?
2. In the question, it is already given like this: d & ((!c <->c)|a). So, in this case I shouldn't write it as: d & (!c <-> (c|a)) even though 'or' binds stronger than '<->'. Is it correct? (Because of Associativity?)

Answer 1

On 1.:

Yes, disjunction has a higher priority than implication. See slide 5. https://es.cs.uni-kl.de/teaching/vrs/slides/VRS-02-PropLogic-1.pdf

On 2.:

I'm not quite sure what you mean. If your red parenthesis are given by the question then of course, you cannot just remove them and apply operator precedence.