2c03-review - 00044

2c03-review - 00044 - b.[5] n T ( n) = 2T ( ) + n 2 2 n n...

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13 b.[5] 2 2 22 2 232 23 4 2 1 12 lg lg lg 2 lg 1 2l g 2 2 2 0 () 2( ) 2 2() 2( ) 2 2 2()2()2 2 2()2 ( )2 2 2() 2 2 1 () ( 1 ( ) ) ( ) ii i i nn n n n i i n Tn T n n TT n n n T n Tn n n n n On n + + = =+ = = = MM 11.[20] Show that the number of Boolean functions of n variables is given by the occurrence T(1)=4 T(n)=(T(n-1)) 2 Solve for T(n). [8] The function f is a Boolean function of n variables if f:{0,1} n {0,1}, where 0 denotes False and 1 denotes True. We know (see any Discrete Math Text) that the number of functions from the set X to {0,1} is equal to the number of subsets of X, i.e. 2 |X| . If X={0,1} n then |X|= 2 n , i.e. |{0,1} n | = 2|{0,1} n-1 |. Denote B(n) = {0,1} n . We have |B(n)|=2|B(n-1)|.
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