ITEC 122 2007fall ibarland

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hw06
Set basics

Although you are welcome to typeset your work nicely (using Microsoft Word or LaTeX or whatever to get nice logic symbols), it's probably much easier to write formulas by hand.

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1. Rosen p.132, #50 (= Rosen 5ed p. 96 #40): bit-string representation.
2. Consider the function dorm, which maps an on-campus RU student to their dorm-building¹ For example, dorm(Jane Doe) = Muse.
   
   1. Is this function onto?
   2. Is it one-to-one?
   3. What if the codomain were all campus buildings, instead of just dorms -- would the function still be one-to-one? onto?
   4. What if the codomain were individual beds in the dorm, instead of just entire dorms -- would the function still be one-to-one? onto?
3. Rosen p146, #2 (= Rosen 5ed p. 108 #2): Is it a function from Z → ℜ?
   (That is, if you put in an integer, will you get out exactly one corresponding real number?)
   1. f(n) = ±n.
   2. f(n) = √(n²+1).
   3. f(n) = 1/(4-n²).
4. Rosen p146, #8 (= Rosen 5ed p. 108 #8): Ceiling, floor
5. Rosen p146, #12 (= Rosen 5ed p. 108 #12): one-to-one?
   1. f(n)=n-1
   2. f(n)=n²+1
   3. f(n)=n³
   4. f(n)=ceiling(n/2)
6. For each of the functions in the previous problem, is f : Z→Z onto?

If you see a few other problems in Rosen which catch your eye, and you'd like to do them for extra credit, you are welcome to (though you can ask me for how much; extra-credit is harder to earn point-per-point than regular credit).

If you write your own html, you might be interested in this page of useful html math (and other) entities

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©2007, Ian Barland, Radford University Last modified 2007.Oct.09 (Tue)

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