Fred wants celebrate his birthday party with as many friends as possbile (Anne, Bernd, Christine, Dirk, Eva). He knows that:
If Bernd and Anne both appear, then Eva will not appear. And Dirk will not appear, if Bernd and Eva both appear. But Eva will appear, if Christine and Dirk appear. On the other hand, Christine will only appear, if Anne also appears. Anne, however, will only appear, if also Bernd or Christine appear.
How many of Fred's friends (and which) will appear at his party in best case?
Sorry for my English, I had to translate everything :p
It's a bit head-aching to read but it might work well if you use variables instead of names and logic operators instead of words.
Let
$$A=\text{Anne appears}\hspace{1cm} B =\text{Bernd appears}\hspace{1cm} C=\text{Christine appears}\hspace{1cm} D =\text{Dirk appears} \hspace{1cm}E = \text{Eva appears}$$
"If Bernd and Anne both appear, then Eva will not appear." $: (B \wedge A) \rightarrow \neg E$
"And Dirk will not appear, if Bernd and Eva both appear." : $(B \wedge E) \rightarrow \neg D$
"But Eva will appear, if Christine and Dirk appear." $(C \wedge D) \rightarrow E$
"On the other hand, Christine will only appear, if Anne also appears." : $A \rightarrow C$
"Anne, however, will only appear, if also Bernd or Christine appear." : $(B \vee C) \rightarrow A$
I might be wrong with the direction of the arrows. But how can I be sure in which direction it goes?
So in the end, those formulas make it much shorter but I cannot quickly say how many people will appear in best case using these formulas. Anything I did wrong till here? And how do you solve this correctly?
Your last two translations are not correct. The next to last should be $C\rightarrow A$ and the last should be $A \rightarrow (B \vee C)$. Now it should be clear that you can have all of $A,C,D,E$ and can't have all five.