For n ≥ 2 , let S_n denote the set of all subsets of \ 1,2 . . ., n\ with no two consecutive numbers. For example \ 1,3,5\ ∈ S_6 , but \ 1,2,4\ S_6 . Then n(~S_5) is equal to ________

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A=\ 1,2,3,4,5 . . . n\ No. of subsets having r elements such that no two are consecutive is = ^ n-r+1 C_r for n=5 , no. of ways = ^ 6 · r C_ r Subsets having no element =1 Subsets having exactly 1 element = ^5 C_1=5 Subsets having exactly 2 element = ^4 C_2=6 Subsets having exactly 3 element = ^3 C_3=1 5+6+1+1=13

For n ≥ 2 , let S_n denote the set of all subsets of \ 1,2 . . .,...

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