three questions dealing with indicator random variables

[trickslapper]

Let E and F be events of a sample space

a. Show that I[sub:3o22yeqb]E?F[/sub:3o22yeqb]=I[sub:3o22yeqb]E[/sub:3o22yeqb]*I[sub:3o22yeqb]F[/sub:3o22yeqb]
b. Under what conditions is it true that I[sub:3o22yeqb]E U F[/sub:3o22yeqb]=I[sub:3o22yeqb]E[/sub:3o22yeqb]+I[sub:3o22yeqb]F[/sub:3o22yeqb]


c. Obtain a general formula I[sub:3o22yeqb]E U F[/sub:3o22yeqb]



Edit: the book has the following answers but i don't know how to get to them:

a. Both I[sub:3o22yeqb]E?F[/sub:3o22yeqb] and I[sub:3o22yeqb]E[/sub:3o22yeqb]*I[sub:3o22yeqb]F[/sub:3o22yeqb] are 1 if E ? F occurs and both are 0 otherwise

b. Events E and F are mutually exclusive

c. I[sub:3o22yeqb]E U F[/sub:3o22yeqb]= I[sub:3o22yeqb]E[/sub:3o22yeqb] + I[sub:3o22yeqb]F[/sub:3o22yeqb]- I[sub:3o22yeqb]E[/sub:3o22yeqb]*I[sub:3o22yeqb]F[/sub:3o22yeqb]

thanks!