Let E, F, G be three events. Findexpressionsfor the events that of E, F, G

a. only F occurs

b. Both E and F but not G occur

c. at least one event occurs

d. at least two events occur

e. all three events occur

f. none occurs

g. at most one occurs

h. at most two occur

The word "expressions" is confusing me a little bit here.

This is what I have right now, but I'm not sure how right it all is:

a. $\displaystyle F\cap(G\cup E)^c$

b. $\displaystyle (E\cap F)\cup G^c)$

c. This is one I'm not sure about, simply because of how long it is

$\displaystyle [(F\cap(G\cup E)^c)\cup (G\cap(F\cup E)^c)\cup (E\cap(G\cup F)^c)\cup((E\cap F)\cup G^c))\cup((E\cap G)\cup F^c))\cup((G\cap F)\cup E^c)) \cup(E\cap F\cap G)]\cap (E \cup F\cup G)^c)$

d.

I don't even want to bother putting the rest in because it just seems like I'm way wrong.