I have the following exercise that I can't really solve or I am not happy with the result:
- If Team A loses, Team B and C will lose too
- If the Teams A and B win, Team C will lose
- If Team B wins, Team A will win too and Team C will lose
- If the Teams B or C lose, Team A will lose too.
How will the games end if these prognoses are right?
First I created the implications and resolved them so that I got $$(A+\overline{BC})*(\bar A+\bar B+\bar C)*(\bar B+A\bar C)*(BC+\bar A)$$
I came to the following result: $$A\bar BC+\bar A\bar B\bar C$$
That would mean that either A wins, B loses and C wins or all the teams lose. But as the last condition is "If the Teams B or C lose, Team A will lose too, this has to be wrong and I think all teams lose. I just can't figure out how to prove this with boolean algebra.
Hope, somebody can help here. Thanks!
Edit: My mistake - just tried it again and the result is as expected: $$\bar A \bar B \bar C$$
Sorry for the inconvenience!