Question 933016
If you mean *[Tex \LARGE P(A\overline{A}) = 1], then it is <font size=6 color="red">false</font>. This is assuming *[Tex \LARGE P(A\overline{A}) = P(A \cap \overline{A})].



Why is it false? Because *[Tex \LARGE P(A\overline{A}) = P(A \cap \overline{A})], this means that is it impossible for both event *[Tex \LARGE A] and event *[Tex \LARGE \overline{A}] to happen. 



The two events are complete opposites of one another. If one happens, then the other does NOT happen. So it *should* really say *[Tex \LARGE P(A\overline{A}) = P(A \cap \overline{A}) = 0]



Again, this is based on the assumption your book is using *[Tex \LARGE P(A\overline{A}) = P(A \cap \overline{A})]