ITEC 122 2008fall ibarland

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hw05
Set basics

1. (3pts) Rosen p119, #4 (= Rosen 5ed p. 85 #4): which are subsets of which?
2. (3pts) Rosen p120, #8 (= Rosen 5ed: p.85 #8): T/F involving ∈ and ⊆
3. (2pts) Rosen: p120, #19 (= Rosen 5ed: p.85 #15):
4. (1pt) Rosen: p120, #24: If A is the set of ITEC courses, and B is the set of ITEC professors, describe A×B.
5. (3pts) Let A = {a,b,c}, B = {5}, and C = {x,y}. What is…
   1. A×C
   2. C×A
   3. C×C
   4. A×B×C
   5. B×B×C
6. (5pts) Rosen p.120 #30:
   Prove that, for any two sets A,B:
        ((A≠B) ∧ (A ≠ φ) ∧ (B ≠ φ)) ⇒ A×B≠B×A.
   (Recall that φ stands for the empty set, {}.)
   Do you need to use all the premises?
   Hint: You'd like to say “Since A≠φ, ∃a∈A. Furthermore, since B≠φ and A≠B, ∃b∈B such that a≠b.” However, this isn't always quite true. How to fix it? How to proceed?
7. (3pts) Rosen p120, #36: Describe each of the following sets more concisely:
   1. { x ∈ N | x³ ≥ 1}
   2. { y ∈ N | y² = 2}
   3. { y ∈ N | y < y² }
8. (3pts) Rosen p.130, #4 (= Rosen 5ed p.94 #4): Practice with ∪, ∩, set-difference.
9. (2pts) Rosen p.130, #26 (= Rosen 5ed p.94 #20): Drawing Venn diagrams

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