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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 noninductive proof is also
possible.
1.
Recursive defnition [13 points]
Give a simple closedform de±nition for each of the following subsets of the real plane.
Give both a precise de±nition using setbuilder 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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 Spring '08
 FLECK@SHAFFER

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