Derive resultant Boolean function

Question

The question goes as follows;

Andreas, Benedikt, Carolin and Dora are invited to a party. Following are known:

When Andreas goes, Benedikt goes as well.
Carolin and Dora are not both going.
Between Andreas and Dora at least one goes.
When Benedikt or Dora goes, Carolin goes as well.

Question asks to draw a boolean table for the above given conditions and derive a resultant Boolean function.

My boolean_table on google spreadsheet (if you wan to edit):

I am quite confused what would be a resultant function (F) here, is it simply OR of all the conditions?

And how can it be deduced who goes the party with the function?

For the resulting function use the AND of all of them, because all of them are supposed to be true — Bram28, Dec 03 '16 at 17:54
@Bram28 thanks, does that mean all of the participants are going? How does second condition go with that. — ro ko, Dec 03 '16 at 18:04
no one goes ... We already know that Carolin and Dora are not going. If Benedikt goes, then CArolin goes, but Carolin does not go, so Benedikt can't go either. And if Andreas goes, then Benedikt goes, but Benedikt does not go, so Andreas does not go either. — Bram28, Dec 03 '16 at 18:09
if we look at the truth table, all goes though. Further more, 3rd condition says one of them must go. It almost looks like conditions are contradicting from each other. Thanks a lot @Bram28 but still bit confusing for me :) https://docs.google.com/spreadsheets/d/1yVl0m_zOCU-wYBixhNdkkaY9QXVxJrEPiJE3RRuNKeQ/edit?usp=sharing — ro ko, Dec 03 '16 at 18:20
So, if you AND all the statements, then they should all work out to 0, because the statements are impossible to satisfy. As I just explained, from statements 1,2, and 4 you dan infer that no one goes, but that contradicts statement 3. — Bram28, Dec 03 '16 at 18:25
$\neg (C \land D)$ should be a $0$ in row 15. Now, when you AND all 4 statements, you indeed get all 0's. Yes, the statements are contradictory! — Bram28, Dec 03 '16 at 18:27
I just noticed something: the third statements talks about Andreas and Dora, and in the table you use $A \land B$ ... Is your symbolization incorrect, or did you write down the wrong statement? — Bram28, Dec 03 '16 at 18:35
@Bram28 Sorry, yes that was a mistake, I was trying to write A ^ D Plus I had D column in sequence which i copied wrong hence the outputs under other columns were wrong. Sorry about all the confusion. I have made the corrections now (on google spread sheet) — ro ko, Dec 03 '16 at 18:42
OK, here is another issue. 'Carolin and Dora are both not going' should be $\neg C \land \neg D' ... Or was the original statement 'Carlin and Dora are not both going'? Because those are different statements! — Bram28, Dec 03 '16 at 18:47

Bram28 · Accepted Answer · 2016-12-03T19:14:09.570

You need to AND all four statements together, since you all statements to be true, i.e. The first should be true AND the second AND the third, AND the fourth.

Unfortunately, you symbolized 'Between Andreas and Dora at least one is going' as $A \vee B$ ... So either that should be $A \vee D$, or you wrote down the wrong statement when you posted you question ...

Also, 'Carolin and Dora both not going' is $\neg C \land \neg D$ which is not the same as $\neg (C \land D)$. So again, eitheryou symbolized ths incorrectly, or you wrote down the wrong statement in your original Question ... Should it be that 'Carolin and Dora are not both going'? If that was the statement you have to work with, then there is no contradiction anymore, so I suspect that is the one.

EDIT Ok, all issues resolved now!

I had quite a few mistakes in there, I corrected everything, which now deduces that andreas, benedict and Carolin three of them goes to the party. — ro ko, Dec 03 '16 at 18:46

Derive resultant Boolean function

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