Subsets S={c1,c2,,xn} Power set:25 ={T TCS) 21= A not-so-combinatorial proof: Let Sn ={1,22,...,2n}and f(n)=25 f(n)=2f(n-1)
Subsets S = {x1, x2,...,xn} Power set: 2S = A not-so-combinatorial proof: Sn = {x1, x2,...,xn} f(n) = 2Sn Let and f(n)=2f(n 1) 2S = {T | T S}
Let Sn {1,22,...,In}and f(n)=25m f(m)=2f(n-1) 25m=U {subsets of Sn that contains n {subsets of Sn that does not contain n 2=|25-|+2-1|=2f(m-1) Sum rule: finite disjoint sets s and T SUT=S+T
Sn = {x1, x2,...,xn} f(n) = 2Sn Let and f(n)=2f(n 1) 2Sn = {subsets of Sn that does not contain xn} {subsets of Sn that contains xn} Sum rule: finite disjoint sets S and T |S T| = |S| + |T| 2Sn = 2Sn1 + 2Sn1 = 2f(n 1)