CS 2233 Discrete Mathematical Structures – Fall 08
10/8/08
4. Homework
Due 10/20/08 before class
Please refer to the corresponding exercise sections in the textbook (Rosen, 6th edition).
2.4 (page 160)
(a) (1 point) 4 a
(b) (1 point) 10 b
(c) (1 point) Use index substitution to rewrite the summation in 15.c such that
the index starts at 0.
3.2 (page 191)
(a) (4 points) 2 a,b,c,d. Justify all your answers by using the definition of
big-Oh to either prove or disprove the claim. You may need to use the fact
that x < 2xwhich is also equivalent to log x < x.
(b) (2 points) 8 a,b. Justify your answers.
(c) (3 points) 22 a,b,c. Use the definitions of big-Oh, Ω, and Θ to prove or
disprove the claims.
(d) (1 point) What is the tight Θ-runtime of the following code snippet? Justify
your answer.
for(i=n; i>5; i=i/2)
print("Hello");
4.1 (page 279)
(a) (3 points) 4 a-e
(b) (3 points) 20 (Use induction on nto prove this claim.)
Extra credit: The question below is for extra credit. Any points earned here may be
applied towards any other homework (in order to increase the homework score to
≥60%).
4.2 (page 291)
(a) (10% points) 38 (Hint: Use strong induction on the number nof cells. Draw
an example picture first, then try to identify “recursive” subcases with fewer
cells that you can use the inductive hypothesis on. This is similar to the
proof for tiling a square with L-shapes.)