(1pt)
Rosen: p120, #24:
If A is the set of ITEC courses, and B is the set of ITEC professors,
describe A×B.
(3pts)
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
(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?
(3pts)
Rosen p120, #36:
Describe each of the following sets more concisely:
{ x ∈ N | x³ ≥ 1}
{ y ∈ N | y² = 2}
{ y ∈ N | y < y² }
(3pts)
Rosen p.130, #4
(= Rosen 5ed p.94 #4):
Practice with ∪, ∩, set-difference.