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Discrete math PROJECT 2-COUNTING SUBSETS (BINARY STRINGS) Choose 6 letters of the English alphabet including all the different characters in your family name. (If you have more than 6 different characters, choose the first 6). Let X be the set of all lower case versions of the letters you have chosen. Let S be the set of all binary strings of length 6 0) Using correct set notation, list the elements in set X (ii) List all the subsets of X with 1 letter. How many such subsets are there? Let x, be the collection of all these subsets. i) List all binary strings of length 6 that include one 1 and seven Os. How many such strings are there? Let S, be the set of all these strings. iv) Construct a bijective function f: x, s, that demonstrates a naturar relationship between x, and Sa- (v) Generalise your function f to a function F:P(x)-S in such a way that F is also a bijection vi) What is IS1 ? That is, how many binary strings of length 6 are there? Use your answer together with your function F to explain the value of IP()
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