Hi, can anyone please help me with this question? Thanks a lot.
Let A, B, and C be any three events. Show that:
(1) if and only if
(2) Given and , determine
For first part, I don't know how to start at all. Plus, with "if and only if", does that mean I need to prove from two directions?
For second part, I did draw Venn Diagram, but still don't feel that is very helpful, except I did find , am I right? What should I do?
Thanks a lot.
Thank you very much, Plato, sorry I was just thinking too much, because I did too much Real Analysis last year, so when I saw that "if and only if" statement, I got scared and thought I need to write heaps of detailed proof. So yes, you are absolutely right, it was just me thinking too much.
May I ask about part 2 again, I calculated the result is just 0.3, in fact can just use 0.8-0.5=0.3, but the only thing is could you please give me advice on how to write about it? Because I feel only use Venn diagram to show is not quite mathematical, could you please tell me if there is anyway to write about it? I did get A U B U C=0.8, but that is really because I worked out from the diagram. Do you think I can do it algebracally? Thanks again.