Let A, B and C be any three events. Show that
(i) if and only if
(ii) Given and , determine
Show that for any two events :
(i) If , then
(ii) If , then
(iii) Why is it incorrect to assume that for some events A and B, and ?
Hello,
I'll give you most of the solution, but you will have to fill in some steps
Thing that may come in handy :
(de Morgan's law)
(de Morgan's law)
From here, it should be very easy to conclude
I'm thinking on this one...(ii) Given and , determine
Show that for any two events :
(i) If , then
why ? because let's consider an element in B. It is contained in A, or it is contained in B, but not in A. This latter possibility gives the set
You can also see that since A and are disjoint, then A and are disjoint.
Hence
And the conclusion follows.
Use (i) :(ii) If , then
but since is a probability, it's
thus
Because is included in(iii) Why is it incorrect to assume that for some events A and B, and ?
By (ii), we should have , which is not the case here