PROBLEM 7 1) Complete the recursive rule for the following recursive definition

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PROBLEM 7 1) Complete the recursive rule for the following recursive definition of a set of all bitstrings a. Base Case A, an empty string, is a bitstring b. Recursive Rule: If s is a bitstring then 2) Complete a recursive definition of function L which determines the bitlength of a bitstring, i.e. if L is well-defined then L(x)-|xl eg. L(1)=1,L(01)-2, L(101)-3, L(1010)=4,etc a. Base Case: ?(A) = 0 b. Recursive Case: your recursive case can have more "if then" clauses] then L(s) = Complete a recursive definition of function rev on bitstrings which reverses the order of bits in a bitstring, e.g. rev(10)-01, rev(1000)-0001, rev(1000111)-1110001, etc a. Base Case 3) rev(l)- A then rev(s) - b. Recursive Case [your recursive case can have more "if then" clauses] 4) Complete a proof by structural induction that for every bitstring s the following holds L( rev(s))- L(s) a. Base Case: i. First just state what you need to argue ii. And now prove it b. Recursive Case: i. First just state what you need to argue ii. And now prove it

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