Math 29 Homework #26 The following quote was hanging outside a restaurant: Good food is not cheap Cheap food is not good Do these two sentences say the same thing or different things? The answer is that logically speaking, they say exactly the same thing; they are both equivalent to the statement that no food is both good and cheap. Though these statements are logically equivalent, I would say that psychologically they suggest different things; when I read the first statement, I picture good expensive food; when I read the second, I picture cheap rotten food. I don't think that my reaction is atypical. Raymond Smullyan

	Reading Read what we covered in today's class: 7.4, 9.4 Read what we will cover in the next class: 9.4, 9.5 When reading 7.4 pay special attention to the following concepts: the definition of simple sets, Theorem 4.2 which notes that simple sets are noncomputable and not c.e., and Theorem 4.3 which establishes the existence of simple sets When reading 9.4 pay special attention to the following concepts: URMO, URMO-computability, Theorem 4.3, note the many later results which come from lifting known URM-results to URMOs When reading 9.5 pay special attention to the following concepts: Turing reducibility, Theorem 5.2, Turing degree

	Problems The following problems are due by the beginning of class on Friday 5/21. p. 141, # 7.4.4.1 p. 142, # 7.4.4.2 p. 142, # 7.4.4.3 p. 173, # 9.4.10.7 p. 173, # 9.4.10.10