Recall that the power sert P(S) of a set S is the
collection of all subsets of S.
For A= {1, 2, 3} and B = {x, y} , calculate the following
cardinalities:
(Please show your work so I can follow along, Thanks!)
1. |P (A) |
2. |P (B) |
3. |A × B2 |
4. |P (A × B) |
5. |P (A) × B|
6. |P (P (A)) |
Recall that the power sert P(S) of a set S is the collection of all subsets...
4. Ranking/Unranking Subsets. Let A be a set of n elements and set Sk(A) be the collection of all k-element subsets of A. Recall that |Sk(A)I - (a.) (8 points) Describe a ranking algorithm to rank a k-element subset of an n-element set. (b.) (8 points) Describe an unranking algorithm to unrank an integer 0 < s< [into a ithm to unrank an integer 0 S s <C) k-element subset of an n-element set. (c.) (10 points) As examples, let...
Show your work, please 4. Partial Orders Let P be the collection of all subsets of X = {a,b,c,d} that have at least two elements. (So {a,c} € P, but {b} P.) Consider the subset relation C as a partial order on P. For example, {a,b} = {a,b,c}. Draw the Hasse diagram, and find any maximum/minimum elements, and maximal/minimal elements.
Let P(X) be the power set of a non-empty set X. For any two subsets A and B of X, define the relation A B on P(X) to mean that A union B = 0 (the empty set). Justify your answer to each of the following? Isreflexive? Explain. Issymmetric? Explain. Istransitive? Explain.
b and c please explian thx i post the question from the book Let 2 be a non-empty set. Let Fo be the collection of all subsets such that either A or AC is finite. (a) Show that Fo is a field. Define for E e Fo the set function P by ¡f E is finite, 0, if E is finite 1, if Ec is finite. P(h-10, (b) If is countably infinite, show P is finitely additive but not-additive. (c)...
Let A={1,2,3,4}. Pick a subset B⊆A uniformly among the 2^4 subsets (i.e. the power set ofA) and let X be its size. Then likewise pick a subset C⊆B uniformly from the power set of B and let Y be its size. Give the joint p.m.f of (X, Y) and compute E(X−Y). Hint: X, Y can take value 0 if you pick the empty set. You can either write down a table or a compact expression of the form P(X=i, Y=j).
Question 4. Suppose S is a collection of subsets in 2 satisfying (ii) If A and B are in S, then An B є s. (a) Given () and (ii), show that the following two conditions are equivalent: (i)IAES, then the complement of A is a finite union of disjoint sets inS (ii) If A, B є s. then the set difference B \A is a finite union of disjont sets in ş (b) Suppose S satisfies (0), (ii), and...
Question 4. Suppose S is a collection of subsets in 2 satisfying (ii) If A and B are in S, then An B є s. (a) Given () and (ii), show that the following two conditions are equivalent: (i)IAES, then the complement of A is a finite union of disjoint sets inS (ii) If A, B є s. then the set difference B \A is a finite union of disjont sets in ş (b) Suppose S satisfies (0), (ii), and...
Question 4. Suppose S is a collection of subsets in 2 satisfying (ii) If A and B are in S, then An B є s. (a) Given () and (ii), show that the following two conditions are equivalent: (i)IAES, then the complement of A is a finite union of disjoint sets inS (ii) If A, B є s. then the set difference B \A is a finite union of disjont sets in ş (b) Suppose S satisfies (0), (ii), and...
Generic set W,X and Y Section 1: Short Answer- Briefly answer each question in the space immediately below it S pts ea. Consider generic sets w, x, and y, and also A-u2-1, 6, 9). B-u,-1, 3, 6. c 3(-1.63) . eenerically. what does P(X) represent? Answer Here 2. Generically, what does / y / represent? 3. (15 pts) RE #a1: Then, generically. I y I : what value? 4. (10 pts) Let W P()3 W yl W? Work this out...
1. Recall that, for a set of alternatives X, a choice structure is a pair (B,C), where B be a collection of subsets of X and C is a function defined on 'B. with C(B) CB for each B E B. C(B) is the set of alternatives chosen when the budget set is B. In the following examples, X = {a,b,c}. (a) State in each of the three cases whether the Weak Axiom of Re- vealed Preferences holds. Provide a...