Consider example 3.4, in the textbook, with the four basic outcomes for the Dow

Question

Consider example 3.4, in the textbook, with the four basic outcomes for the Dow Jones Industrial Average (DJIA) over 2 consecutive days: O1 : The DJIA rises on both days O2 : The DJIA rises on the first day but doesn't rise on the second day O3 : The DJIA rises on the second day but doesn't rise on the first day O4 : The DJIA doesn't rise on either day Let events A and B be the following: A: The DJIA rises on the first day B: The DJIA rises on the second day a. Show that (A B) (A B) = B b. show that A (A B) = A B

Explanation / Answer

Note: U stands for "or" and n (intersection) stands for "and"

a) Hence (AnB) U (Abar n B) means (DJIA rises on day 1 and on day 2) or (DJIA falls on day 1 and DJIA rises on day 2) => DJIA rises on day 2 and (DJIA rises or falls on day 1)

= DJIA rises on day 2 = B

Hence proved.

b) A U (Abar n B) means DJIA rises on day 1 or (DJIA falls on day 1 and DJIA rises on day 2) =  (DJIA rises on day 1 or  DJIA falls on day 1) and  (DJIA rises on day 1 or  DJIA rises on day 2) = DJIA rises on day 1 or DJIA rises on day 2 = A U B

Hence proved

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