MAT 243 Online Written Homework Assignments for Week 7 (units 19-21) 1. Western Digital gives the rate of non-recoverable read errors per bits read of its 8 TB WD80EFZX hard drive as less than 1 in 1014 . Suppose such a drive is full. What can you say about the probability of encountering at least one non-recoverable read error while copying the entire drive, based on this information? a. Give the exact answer and explain it. Consider that hard drive manufacturers use decimal, not binary prefixes in their capacity specifications, i.e. 1 TB is one trillion (1012 ) bytes. b. Give a decimal approximation of the probability in a. using the calculus fact that (1 + ) for small || and large integers n. You may give your answer as a percentage. 2. Suppose is the set of integers greater than 1, and is the following relation on : if and only if and share a prime factor. Answer the following questions and explain your answers. a. b. c. d. Is reflexive? Is anti-symmetric? Is symmetric? Is transitive? 3. Let = and be the relation defined by = {(, ) | }. a. Identify the relation . b. Find 2 and prove your answer. 2017 R. Boerner ASU School of Mathematical and Statistical Sciences