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Let S = 1 , 2 , 3 , 4 , 5 , 6 . Then the number of oneone functions f : S → P ( S ) , where P ( S ) denote the power set of S , such that f ( n ) ⊂ f ( m ) where n < m is

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3240

Step-by-step solution

Let S = 1 , 2 , 3 , 4 , 5 , 6 , then the number of one-one functions, f : S · P ( S ) , where P ( S ) denotes the power set of S , such that f ( n ) < f ( m ) where n < m is n ( S ) = 6 P S = ϕ , 1 , … 6 , 1 , 2 , … , 5 , 6 , … , 1 , 2 , 3 , 4 , 5 , 6 Case - 1 f ( 5 ) = any 5 element subset A of S i.e. 6 choices f ( 4 ) = any 4 element subset B of A   i.e. 5 choices f ( 3 ) = any 3 element subset C of B i.e. 4 choices f ( 2 ) = any 2 element subset D of C i.e. 3 choices f (

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