List all of the proper subsets of the set A = {10, 2}
a) ∅, {10}, {2}, {10, 2}
b) ∅, {10}, {2}
c) ∅, {10}, {2}, {10, 2}, {2, 10}
d) {10}, {2}
e) {10}, {2}, {10, 2}
f) None of the above.
List all of the proper subsets of the set A = {10, 2} a) ∅, {10},...
Calculate the number of subsets and the number of proper subsets for the set. 9) 9) 1, 3,5,7,9,11) A) 63; 62 B) 64; 63 C) 63; 64 D) 62; 63
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...
2. Given the set S-ta,b,c,d,e,f,g,h) a) How many subsets does S have? b) How many subsets have exactly 5 elements? c) A subset is randomly chosen for the collection of all possible a) b) c) subsets. What is the probability that it contains exactly 3 elements? d) A subset is chosen at random from all the subsets. d) What is the probability that it contains the element a?
Question 5 16 pts Let set A = {a,b,c} Which of the following are proper subsets of A? {a} a, b {a, b} {a,b,c} {d} Question 6 10 pts Let A = {ne Z | n = 6a + 4 for some integer a} Let B = {me Z m = 18b - 2 for some integer b} Prove or disprove that ASB Hint: follow the method used in Example 6.1.2 on page 338 of the text. HTML Editora B...
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)...
Prove that all sets with n elements have 2n subsets. Countthe empty set ∅ and the whole set as subsets.
4) Let D be the set of all finite subsets of positive integers. Define a function (:2 - D as follows: For each positive integer n, f(n) =the set of positive divisors of n. Find the following f (1), f(17) and f(18). Is f one-to-one? Prove or give a counterexample.
41. How many subsets does the set {a, b, c, d, e,f} have?
5-13 please
Homework on sets 1. let the universe be the set U (1,23. .,1.0), A (147,10), B- (1,2 list the elements for the following sets. a. B'nt C-A) b. B-A c. ΒΔΑ 2. Show that A (3,2,1] and B (1,2,3) are equal 3. Show that X Ixe Rand x > 0 and x < 3j and ( 1,2) are equal. 5. Use a Ven diagram and shade the given set. (cnA)-(B-Arnc) Show that A (x| x3-2x2-x+2 O) is not...
Let S be the set of all subsets of Z. Define a relation,∼, on S by “two subsets A and B of Z are equivalent,A∼B, if A⊆B.” Prove or disprove each of the following statements: (a)∼is reflexive(b)∼is symmetric(c)∼is transitive