The statement we end up with, "All people who do not win lotteries are people who do not get lots of mail," is false.
We first find the contrapositive by switching the hypothesis and conclusion and then negating both:
"All people who do not get lots of mail are people who do not win lotteries."
The contrapositive of a true statement is true.
From here we find the converse by switching the hypothesis and conclusion of the newest statement:
"All people who do not win lotteries are people who do not get lots of mail."
This is essentially a negation of the original statement; a negation of a true statement is false.
