$1.$ I did not buy a lottery ticket this week.
$2.$ Either I bought a lottery ticket this week or won the million dollar jackpot or both
$(or)$
I bought a lottery ticket this week or won the million dollar jackpot or both .
https://math.stackexchange.com/questions/2130327/does-either-make-an-exclusive-or
$3.$ If I bought a lottery ticket this week then I won the million dollar jackpot.
$4.$ I bought a lottery ticket this week and won the million dollar jackpot.
$5.$ I bought a lottery ticket this week if and only if I won the million dollar jackpot.
$6.$ If I did not buy a lottery ticket this week then I did not win the million dollar jackpot.
$7.$ I did not buy a lottery ticket this week and I did not win the million dollar jackpot .
$8.$ I did not buy a lottery ticket this week or I bought a lottery ticket this week and won the million dollar jackpot .