Suppose we take our universe to be the set U = { 1, 2, 3, 4, 5, . . . , 20 }, and set A = { x | x ∈ U and x is odd } C = { x | x ∈ U and x is a square } B = { x | x ∈ U and x is prime } D = { x | x ∈ U and x = 3n − 2 for some n ∈ N } (a) Express each of the above sets using the list method. (b) Use the descriptions from (a) to determine each of the following. Use the list method. i. A ∪ B. ii. A − B. iii. B ∩ D iv. D. v. A ∩ C. vi. B ∪ C.

Q: Let A = {x € N|x < 7}, B = {x € Z] -4 < x-2<4}. And C = {x E R|x² + x - 12 = 0}. a) List the…

A:

Q: is obtained at least twice? (b) How many times must two dice be rolled to guarantee that score is…

A: *answer:    Consider Now in order to show thatandhave the same cardinality,…

Q: Find an example to each of the following: a) Sequences {Xn} and {Yn} such that they are both…

A:

Q: What is the cardinality of the set of 2 x 2 matrices over N? Prove your answer.  Note: a 2 x 2…

A:

Q: (9) Let n and k be positive integers. Recall from lecture that a weak composition of n into k parts…

A: 9.For  be positive integers, a weak composition of  into  parts is a -tuple  of nonnegative integers…

Q: Give an example of a partition S of [-1, 1] that satisfies all the following requirements: •|S| = 5…

A:

Q: 2 -1 Let A = Show that the equation -6 3 b2 Ax = b does not have a solution for all possible b, and…

A:

Q: Prove that ∀a, b, k ∈ Z that ((4|k) ∧ (k = ab)) ⇒ (2|a ∨ 2|b)

A:

Q: let A= {y is an element of Z; y=6b-4 for some integer b} B= {x is an element of Z; x=3a+2 for some…

A:

Q: Prove that essays (a) If A is open and B is closed, then A - B is open; (b) If A is closed and B is…

A:

Q: Show that [0, 1] nQ and Q have the same cardinality.

A:

Q: Is {1} proper subset of A  A={x,{y},1,2,3,{2,3},{3}}

A: A proper subset of a set A is a subset of A that is not equal to A.Or in other words, if B is a…

Q: Find all of the units in Pn and verify where Pn is the power set of the set {1,2,...,n} with…

A: Find all of the units in  and verify where is the power set of the set  with addition defined as…

Q: Prove that if A ⊆ B and both sets have minima then min B ≤ min A

A:

Q: A = {n EU | n is odd} and B = {n € U | 2n + 1 is a prime number}. Compute the size of the following…

A: Given Information: U=1,2,3,4,5,6,7,8,9 A=n∈U | n is odd B=n∈U | 2n+1 is a prime number

Q: Consider the following sets: A = {1, 2, 3) B = {x,y} Z = the set of all integers Which claim is…

A:

Q: When |S| denotes the number of elements of the set S, and S = {x/1 ≤ x ≤ 100, x € integer } There…

A:

Q: 1) What is the following recursive set S? • 3 ∈ S • x,y ∈ S → (x + y) ∈ S

A: (Solving the first question as per our guidelines) Question: What is the following recursive set S?…