DISCRETE MATH: Describe all subsets of ℕ w/ 3 as lower bound w.r.t. order |

[NookLines]

Hello!

I need some help on these questions if it's not too much problem (they're not homework problems, no worries; I'm studying for an exam)


a) Describe all subsets of ℕ for which 3 is a lower bound with respect to the order |.

b) Let p be a positive prime number. How many subsets of ℕ arethere with p as an upper bound with respect to the order |?

c) Give examples of at least three different equivalence relations on

.

d) Describe strategies to prove the following: (b) A = ∅. (d) The set A has one single element. (omitted two of them cause I knew how to do them)

 

[stapel]

a) Describe all subsets of \(\displaystyle \, \mathbb{N}\,\) for which 3 is a lower bound with respect to the order |.

What is the "order" represented by the "pipe" character? What is your book's definition of "lower bound"? Does your book include zero within the natural numbers? (Usually, it isn't, but I'm checking.) How have you attempted to apply this information?

b) Let p be a positive prime number. How many subsets of \(\displaystyle \, \mathbb{N}\,\) are there with p as an upper bound with respect to the order |?

What is your book's definition of "upper bound"? How have you attempted to apply this information?

c) Give examples of at least three different equivalence relations on \(\displaystyle \, \mathbb{Z}\,\).

What is your book's definition of an "equivalence relation"? How have you attempted to apply what you've learned from the book's examples to this exercise?

d) Describe strategies to prove the following: (b) A = \(\displaystyle \, \emptyset.\)\, (d) The set A has one single element. (omitted two of them cause I knew how to do them)

What is the set "A"?

Please be complete. Thank you!

 

[NookLines]

What is the set "A"?

Please be complete. Thank you!

Hi! For now I'm going to answer this part of your question before I get to the others. We're actually not given what set A is! I think we're just supposed to come up with a general "What would you do given you had to prove a set is empty". I have a vague idea now (I have to prove the set is unique right?) but I'd like an example of this to see :S

Thanks for responding!