JHU-CTY Theory of Computation (TCOM) Lancaster 2007 ~ Instructors Kayla Jacobs & Adam Groce
MATH REVIEW PROBLEMS
(1) Simple Set Theory
Fill in the blanks with , ,
,
, =, or ≠:
42
_______ {2, 4, 6, 8, 10, …}
42
_______ {2, 4, 6, 8, 10}
{42} _______ {2, 4, 6, 8, 10, …}
_______
{42} _______
_______
3/2 _______
3/2 _______
3/2 _______
{x | x is the answer to Life, the Universe, and Everything}
(2) Combinations Fun
How many 9-letter strings (that may or may not be actual English words) can you make by
rearranging letters of the word KALAMAZOO? (Note: You can leave factorials in your answer.)
(3) Prove It!
a) Prove that 1 + 3 + 5 + 7 + … + (2n-1) = n2. What proof technique did you use?
(continued)
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JHU-CTY Theory of Computation (TCOM) Lancaster 2007 ~ Instructors Kayla Jacobs & Adam Groce
(continued)
b) Prove that there are at least two people at CTY Lancaster (population ~500) with the same
birthday. What proof technique did you use?
c) Prove that the cube root of 2 is irrational. What proof technique did you use?
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