Question

If a finite set A has m elements, then the number of non-empty proper subset of A is 

(1) 2^m 

(2) 2^m – 1 

(3) 2^{m - 1} 

(4) 2(2^{m - 1} – 1)

Answer 1

(4) 2(2^{m - 1} – 1) 

P(A) = 2m 

Proper non empty subset = 2m – 2 = 2(2^{m - 1} – 1)