# hw1 - MCS4653 Theory of Computation Homework Assignment 1...

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MCS4653, Theory of Computation Homework Assignment 1, Due 9/15/03 Name Student ID Page 1 1. (Sudkamp 1.2) Let X = { a,b,c } and Y = { 1 , 2 } . a) List all the subsets of X . b) List the members of X × Y . c) List all total functions from Y to X . 2. (Sudkamp 1.3) Give functions f : N N that satisfy a) f is total and one-to-one but not onto. b) f is total and onto but not one-to-one. c) f is not total, but is onto. 3. (Sudkamp 1.17) Prove that the set of real numbers in the interval [0 , 1] is uncountable. Hint: Use the diag- onalization argument on the decimal expansion of real numbers. Be sure that each number is represented by only one inﬁnite decimal expansion.

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Unformatted text preview: MCS4653, Theory of Computation Homework Assignment 1, Due 9/15/03 Name Student ID Page 2 4. (Sudkamp 1.41) Using the tree below, give the values of each of the items in parts ( a ) to ( e ). x 14 x 10 x 5 x 6 x 11 x 7 x 2 x 3 x 8 x 12 x 15 x 16 x 13 x 9 x 4 x 1 a) the depth of the tree b) the ancestors of x 11 c) the minimal common ancestor of x 14 and x 11 , of x 15 and x 11 d) the subtree generated by x 2 e) the frontier of the tree 5. (Sudkamp 1.42) Prove that a strictly binary tree with n leaves contains 2 n-1 nodes....
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hw1 - MCS4653 Theory of Computation Homework Assignment 1...

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