1 def subset2binary (A, B): "" "Binary encoding of a subset A subset A of a finite set B may be encoded as a binary number as follows - consider a binary number of length n, where n is the size of B 4 5 - artificially impose an order to the elements of B (since we already have represented the set using a list, this is trivial: use the order imposed by the list) - using this order, associate a bit of the binary number with each element of B (the first bit with the first element, the second bit with the second element, the ith with the ith) - considereach element of B if it is in A, the associated bit of the binary number is 1, otherwise (or perhaps else?) the associated bit of the binary number is beautiful, a subset may now be encoded by a binary number 19 20 21 Note that this encoding is an elegant way to prove that the powerset of a set of size n must be of size 2n: there are 24n binary numbers of length n and there is a 1-1 correspondence between binary numbers of length n and subsets of a set of size n, 23 24 as established by this function, so there are 2 n subsets of a set of size 25 26 27 and the powerset is a *very* important concept. 28 29 30 31 >> subset2binary ([], C1]) 32 33 >> subset2binary ([42], [5, 2, 3, 42]) 34 35 >> subset2binary ([0,2,4], [0, 1, 2, 3, 4, 5]) 36 37 38 39 40 41 so the powerset of a set of size n is of size 2n It is useful to have mutiple proofs of important concepts, You will explore the powerset more deeply in cs250, and then see the full fruition of its importance in CS350 0001' 101010 Params: A (list): set of integers, represented internally as a list; A is a subset of B B (list): finite set of integers, represented internally as a list, you may assume B is not empty 43 Returns: (string): binary number, represented internally as a string, associated with the subset A in B 45 46 pass # ADD YOUR CODE HERE, REPLACING pass 48