- Exercises taken from Discrete Mathematics and its Applications,
Seventh Edition unless otherwise noted.
- You must show all of your work for each problem!
- Points will be deducted if you do not show all of your work.
- Each problem is generally worth 10 points.
Problems with multiple parts may be assigned more points if there are enough parts or
each part is significant enough.
- The Review Questions are always related to the section that will be discussed on the assignment due date.
|1.2||40||Look at #41 to see what sort of answer it is looking for.
|1.3||58||Briefly describe how you arrived at your answer.
|1.4||32||See the solution to #33 for an example of what it is asking for. In particular, for each one you need to:|
(This one is worth 20 points)
- Specify the domain and define appropriate predicate(s).
- Express the statement using your predicate(s) and the appropriate quantifier(s).
- Negate the expression and then move the negation as far to the right as you can.
- Express the negation in English, phrasing it "nicely".
|1.7||2||Be very precise, using the definition of even (In particular, you cannot not say, for instance, that 10x+14y-6z+12 is even. You must use algebra to make it look like 2k for some integer k. Similarly for future problems with either odd or even.). A common mistake on this kind of proof is to write it in such a way that you are essentially assuming the two numbers are the same number without realizing it.
|16||As with the previous problem, make sure you don't construct a proof that only ends up proving it for m=n.
|Review Question||12||On page 111|