Consider Example 3.4, with the following four basic outcomes for the Dow Jones Industrial Average over two consecutive days:
O1: The Dow Jones average rises on both days.
O2: The Dow Jones average rises on the first day but does not rise on the second day.
O3: The Dow Jones average does not rise on the first day but rises on the second day.
O4: The Dow Jones average does not rise on either day.
Let events A and B be the following:
A: The Dow Jones average rises on the first day.
B: The Dow Jones average rises on the second day.
a. Show that (A ∩ B) ( (A ∩ B) = B.
b. Show that A ( (A ∩ B) = A ( B.