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 1A  B2  1A  B2 = B.

b. Show that A  1A  B2 = A  B.