A set is known to have 255 proper subsets. How many distinct elements does this set have?

Answer 1

by proper subsets I assume we would exclude the empty set
So with the empty set there were 256 subsets

for n elements, the number of subsets is 2^n
2^n = 256
but 256 = 2^8
so n = 8

and there were 8 elements in the set

Answer 2

255

Answer 3

Yes

Answer 4

2^8