consider the sets A ={ 2,11,13} and B = {-1, 0, 11} find the following sets....
1. Consider the sets: A = {a, b, c, d, e, f, h, j}, B = {a, b, i }, C = {f, h} and U = {a,b,c,d,e,f,g, h,i,j} a. Draw a Venn diagram and place each element in its appropriate region. Insert a photo of your diagram into your HW document. b. Is C a subset of A? Why? C. Is C a subset of B? Why? d. Is A a subset of B? Why? e. Are B and...
1. Find the supremum and infimum of the following sets. (c) { (a) {, e} (b) (0,1) :n € N} (d) {r EQ : p2 <4} (e) [0, 1] nQ (f) {x2 : x € R} (8) N=1 (1 – 7,1+) (h) U-[2-7-1, 2”)
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...
1. Do the following problems: a. Find the sets A and B, if A-B = {1, 5, 7, 8), B-A = {2, 10} and An B = {3, 6, 9). b. Draw a Venn Diagram for the Symmetric Difference of the sets A and B. c. Find and list all the partitions of S = {a,b,c,d,e).
Sets A, B, and Care subsets of the universal set U. These sets are defined as follows. U= {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {1,6,7,8,9} B = {1, 3, 4, 7, 9) C = {4, 5, 6, 7} Find CU ( BA)'. Write your answer in roster form or as Ø. CU (BNA): = 0 Х 5 ?
Consider the following venn diagram with universal set, U, and sets A and B. The numbers in the diagram give the COUNTS of elements in the region. Assume we know that: n(U)=196 Consider the following venn diagram with universal set, U, and sets A and B. The numbers in the diagram give the COUNTS of elements in the region. Assume we know that: n(U) 196 Ul 37 79 69 Find each of the following: ROUND TO THREE DECIMAL PLACES! P(A)-...
Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} be the universal set. Consider the two subsets A = {0, 2, 4, 6, 8} and B = {0,3,6,9}. Use the roster method to write each of the following sets (a) AUB. (b) An B. (c) AC. (d) (AUB) – AC
2. Determine whether the given sets are countable or uncountable. Justify each answer with a bijection (or table like we did with Q+) or using results from class/textbook. (a) {0, 1, 2} * N (b) A = {(x, y) : x2 + y2 = 1} (c) {0, 1} R Che set of all 2-element subsets of N (e) Real numbers with decimal representations consists of all 1s. (f) The set of all functions from {0,1} to N
C++ program which partitions n positive integers into two disjoint sets with the same sum. Consider all possible subsets of the input numbers. This is the sample Input 1 6 3 5 20 7 1 14 Output 1 Equal Set: 1 3 7 14 This is the sample Input 2 5 10 8 6 4 2 Output 2 Equal Set: 0
(a) Suppose that A1,..., All is a collection of k > 2 sets. Show that U412 4:1 - L140.4jl. i=1 {ij} where the second term on the right sums over all subsets of [k] of size 2. [Hint: Use induction on k] (b) Deduce that in every collection of 5 subsets of size 6 drawn from {1,2,..., 15}, at least two of the subsets must intersect in at least two points. (c) Show that the inequality in (a) is an...