#### Answer

a) I did not buy a lottery ticket this week.
b) I bought a lottery ticket this week, and I won the million dollar jackpot!
c) If I bought a lottery ticket this week, I won the million dollar jackpot.
d) I either bought a lottery ticket this week or I won the million dollar jackpot.
e) If I won the million dollar jackpot I bought a lottery ticket this week, and if I bought a lottery ticket this week I won the million dollar jackpot.
f) If I did not buy a lottery ticket this week, I did not win the million dollar jackpot.
g) I either did not buy a lottery ticket this week or I did not win the million dollar jackpot.
h) If I bought a lottery ticket this week, I won the million dollar jackpot; otherwise, I did not buy a ticket.

#### Work Step by Step

To solve this problem, the task is to incorporate "I bought a lottery ticket this week" for p and "I won the million dollar jackpot" for q so that the proposition makes sense in English.