The usages of the word "prefer"
The following are sentences I wrote about the usages of the word "prefer". I know that sentence a and b are correct, because they are standard usages. But, I am not sure if sentence c, d, and e are also correct or not. Could anyone please help me with this? Thank you!
a. I prefer to win rather than (to) lose.
b. I prefer winning to losing.
c. I prefer to win instead of losing.
d. I prefer winning instead of losing.
e. I prefer winning rather than losing.