Implication Operator I think I fail to understand why I might be wrong in the way I translate the following formulas in English.
D stand for 'I will eat'

R stand for 'I will drink'



*

*¬R -> ¬D
My answer: I will not eat if I will not drink.
Because of order of precedence and the not operator goes first:
Could be: I will not eat, I will not drink therefore.


*¬(D ∧¬R )
My answer: I will not eat and I will drink.
I think:
The operation in the parenthesis evaluates to false.
Could it be: I will eat and I will not drink. ?
thank you for looking at the problem.
Update:
Possible answer for the second question:
I will drink and I will eat.
logic:
evaluation in the () is false

Second update
As per comment I am still missing out and I should read on De Morgan's laws
not() => true
If i remove the parentheses I would have:
Possible answer:
I will not eat and I will not drink. 

*

*D stand for 'I will eat'

*R stand for 'I will drink' \begin{equation}\tag{1} \lnot R\rightarrow \lnot D \end{equation} \begin{equation}\tag{2} \lnot(D\land\lnot R) \end{equation}
Your first answers are correct, although I had to read your second attempt twice before I understood the meaning. I would personally write $(1)$ as "If I will not drink, then I will not eat".
In general, when it's not that case that two things ($D$ and $\lnot R$) are true, at least one of them is false. This means the English translation of $(2)$ would be "Either I will drink, or I will not eat, or both".
