From initial topic to finished paper #### Posted Assignments

For (X, Sp) defined in each of the following exercises, describe all independent subsets of X (as…

by | Apr 22, 2023 | Posted Assignments

For (X, Sp) defined in each of the following exercises, describe all independent subsets of X (as defined in D4). (a) Exc. 2; (b) Exc. 3; (c) Exc. 4; (d) Exc. 5; (e) Exc. 6; (f) Exc. 7.

Exercise 2

Let X be any set, and define Sp(S) = ∅ for all S ⊆ X. Which axioms for an independence structure hold?

Exercise 3

Let X be any set, and define Sp(S) = S for all S ⊆ X. Which axioms for an independence structure hold?

Exercise 4

Let X be any set, and define Sp(S) = X for all S ⊆ X. Which axioms for an independence structure hold?

Exercise 5

Uniform Independence Structures. (a) Let X be any set, and fix k ∈ ℕ+. For S ⊆ X, define Sp(S) = S if |S|

Exercise 6

Independence Structure for a Set Partition. Suppose I is an index set, {Ti : i ∈ I} are given pairwise disjoint nonempty sets, and X = S i∈I Ti . Given S ⊆ X, define Sp(S) to be the union of all Tj ’s such that S ∩ Tj ≠ ∅. Prove that axioms A0 through A4 hold.

Exercise 7

Let X = ℝ, and for each S ⊆ X, let Sp(S) = the closure of S in the real line. (By definition, given z ∈ ℝ and S ⊆ ℝ, z ∈ iff for all ε > 0, the open interval (z − ε, z + ε) intersects S.) Which axioms for an independence structure hold?

#### HOME TO CERTIFIED WRITERS #### Why Place An Order With Us?

• Certified Editors
• Profesional Research
• Easy to Use System Interface
• Student Friendly Pricing

#### Have a similar question?

##### Services that we offer

Your Paper Is In Safe Hands

PLAGIRAISM FREE PAPERS

All papers we provide are well-researched, properly formatted and cited.

TOP QUALITY

All papers we provide are well-researched, properly formatted and cited.

HIGHLY SECURED

All papers we provide are well-researched, properly formatted and cited.