hw6 - CS 173: Discrete Structures, Fall 2010 Homework 6...

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CS 173: Discrete Structures, Fall 2010 Homework 6 This homework contains 5 problems worth a total of 54 points. It is due on Friday, October 15 at 4:00 PM. Put your homework in the appropriate dropbox in the Siebel basement. Since the main point of this assignment is to learn how to write proofs by induction, you must use this proof technique when the problem says to use it, even if a non-inductive proof is also possible. 1. Recursive defnition [13 points] Give a simple closed-form de±nition for each of the following subsets of the real plane. Give both a precise de±nition using set-builder notation and also an informal geometrical description using a picture and/or words. (a) (4 points) The set T de±ned by: i. (1 , 1) T . ii. If ( x, y ) T , then ( x + 1 , y + 1) T . iii. If ( x, y ) T , then ( x + 2 , y ) T . iv. If ( x, y ) T , then ( x, y + 2) T . (b) (4 points) The set T R 2 de±ned by: i. (0 , 0) T . ii. If (
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hw6 - CS 173: Discrete Structures, Fall 2010 Homework 6...

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