CMPSCI 250: Introduction to Computation

David Mix Barrington

Spring, 2012

Homework Assignment #4

Posted Friday 2 March 2012

Due on paper in lecture, Friday 9 March 2012.

There are eight questions for 60 total points plus 10 extra credit. All but two are from the textbook, Mathematical Foundation for Computer Science. Note that the book has both Exercises and Problems -- make sure you are doing a Problem and not the Exercise with the same number. The number in parentheses following each problem is its individual point value.

Students are responsible for understanding and following the academic honesty policies indicated on this page.

Correction in purple (to Problem D-1) added 5 March.

Correction in green (to Problem 3.6.2) added 6 March.

Correction in orange (again to D-1) added 9 March.

• Problem 3.5.1 (5)

• Problem 3.6.2 (5) Instead of "any number" it should say "any positive natural". You can't write zero or negative integers as products of prime powers.

• Problem 4.1.3 (10)

• Problem 4.3.1 (10)

• Problem D-1 (10): Let S(n) be the sum, for i from 1 through n, of (-1)ⁱi². For example, S(4) = -1 + 4 - 9 + 16 = 10. Find a polynomial whose value is S(n) and prove by induction that your result is correct. (Your polynomial may include a (-1)ⁿ, for example.)

• Problem 4.4.4 (10)

• Problem 4.4.5 (10)

• Problem D-2 (10XC) Prove by induction that the number of possible Hasse diagrams for the relation S in Problem 2.10.5 (d) is 2^n-2, where n is the number of teams in the tournament.

Last modified 9 March 2012