home—info—lectures—hws—exams
hw05
Set basics
Due 2007.Sep.28 (Fri) noon
Although you are welcome to typeset your work nicely (using Microsoft Word
or LaTeX or whatever to get nice logic symbols),
it's probably much easier to write formulas by hand.
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Here's a screen shot.
-
Rosen p119, #4
(= Rosen 5ed p. 85 #4):
which are subsets of which?
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Rosen p120, #8
(= Rosen 5ed: p.85 #8):
T/F involving ∈ and ⊆
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Rosen: p120, #19
(= Rosen 5ed: p.85 #15):
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Rosen: p120, #24:
If A is the set of ITEC courses, and B is the set of ITEC professors,
describe A×B.
-
Let A = {a,b,c}, B = {5}, and C = {x,y}.
What is…
- A×C
- C×A
- C×C
- A×B×C
- B×B×C
- Recommended extra-credit: Rosen pl.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?
-
Rosen p120, #36:
Describe each of the following sets more concisely:
- { x ∈ ℜ | x³ ≥ 1}
- { y ∈ ℜ | y² = 2}
- { y ∈ ℜ | y < y² }
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Rosen p.130, #4
(= Rosen 5ed p.94 #4):
Practice with ∪, ∩, set-difference.
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Rosen p.130, #26
(= Rosen 5ed p.94 #20):
Drawing Venn diagrams
If you see a few other problems in Rosen which catch your eye,
and you'd like to do them for extra credit, you are welcome to
(though you can ask me for how much; extra-credit is harder to earn
point-per-point than regular credit).
If you write your own html, you might be interested in this
page of useful html math (and other) entities
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