回复：请适当陈述归纳法,直接法,对应法.

直接法:a1,a2,...an
1 empt set,c(n,0)
c(n,1)sets only one element
...
c(n,m)sets m lements
...
c(n,n)set n elements.
So,we have c(n,0)+....+c(n,n)=(1+1)^n=2^n
对应法:If the subset has ai let it to 1,don't has to 0.
WE have 1 to 1 subset to f1f2...fn. fi is 1 or 0.
empty set to 00.....0,.......{a1a2....an} to 11...1.
So,we have 2^n by binary.
归纳法is trival,...miss...