NOTE 1: Be sure to read Homework Format and Homework Writing Policy BEFORE writing up your solutions to be turned in.
NOTE 2: When two or more Lessons are to be turned in on the same day, please staple the Lessons separately and turn them in separately.
Due Monday, February 25
- Sect. 6:
- 6.11(a)*(d)**, 6.27(b)(d)***
* For 6.11(a), give precise proofs or counterexamples. The proofs should be given in the standard way for proving universally quantified statements.
NOTE: The statement “x divides y” means (in this context) “there exists a natural number k such that y = kx”. (Note that the definition of “divides” contains no reference to “division”. It is purely a multiplicative property: “x divides y” means the same as “x is a factor of y”, which is the same as “y is a multiple of x”.)
PLEASE READ, UNDERSTAND, AND DIGEST THE PRECEDING DEFINITION!
** For 6.11(d), think only about reflexive and symmetric at this time (transitive may be dealt with in a later lesson). Give a complete proof; since this set consists of a small number of specific elements, you will be dealing with them specifically.
***For 6.27(b)(d), give a precise proof or counterexample. A proof should be given in the standard way for proving universally quantified statements.
NOTE: As stated on the Course Home Page, all due dates are tentative. Assignments, or parts of assignments, may be postponed to a later date.
Last modified Feb 25, 2008 9:09 PM
Go to Lesson 21 (due Feb 25).
Go to Lesson 20a (due Feb 29).
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