The Universal set U is consists of all odd numbers below one and 50; A is a set  of all x's such that x is divisible by five; B is a set of all x's such that x is prime number; C is a set of all x's such that x is divisible by 3. Find: A ∪ B A ∩ B A ∩ C B ∩ C A ∩ B ∩ C

Q: Find the sup and inf of the following set ∩(1 − 1/n, 2 + 1/n) where n ∈ N

A: The problem is asking us to find the supremum (least upper bound) and infimum (greatest lower bound)…

Q: 1. Given that Z denotes the set of all integers and N the set of all natural numbers, describe each…

A: Given that Z denoted the set of all integers, N denotes set of all natural numbers. To describe each…

Q: prove that any set S subset of {1,2,,...100} with |S|=26 contains at least one odd number or it…

A: We have a subset S of {1,2,.......,100} with |S| = 26. We have to prove that S contains at least one…

Q: Define the following sets: A = {1,3,7,9,10} B = {2,5,7,8,9,10) C = {0,1,3,10} D = {2,4,6,8,10) E =…

A: Given, D={2,4,6,8,10} E={x\x is negative natural number} That is E={-1,-2,-3....} Therefore…

Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

A:

Q: For the given sets A and B, find A∩ B, A∪ B, and Ac (the complement of A). A and B are subsets of…

A: We need to find A Intersection B                               A union B…

Q: Let A be a set. What does it mean for A to be uncountable? Select one: There is no way to assign a…

A:

Q: Find an infinite set A such that a. A is finite and b. A is infinite. Use the real numbers R as the…

A:

Q: The Universal set U is set of all odd numbers between 1 and 50; A is a set of all x's such that x is…

A:

Q: . Prove the following statement: For all integers x and y, if x and y are both even, then xy is…

A:

Q: Define the following sets: A = {1,3,7,9,10} B = {2,5,7,8,9,10} E = {x: x is a negative natural…

A:

Q: S SC equals SC none of these Question 3 (1 point) Saved Listen Given: Set S consists of all positive…

A: 2)    S 3)    divisible by 18

Q: Complete the sentences below so as to obtain correct claims, by writing into each empty space an…

A: According to our policy, we answer only the first three subdivisions. For the remaining…

Q: The universal set U is defined as the set of positive integers less than 10. The subsets A and B are…

A:

Q: Prove or disprove: Let n ∈ Z. If n is odd, then there are odd integers a, b, and c, with a + b + c…

A:

Q: Let the universal set be ℝ, the set of all real numbers, and let  A = {x  ℝ | −3 ≤ x ≤ 0}, B = {x…

A:

Q: |(A ∪ B)\(C ∪ D)|

A: We have to give a formula for |(A ∪ B)\(C ∪ D)| in terms of the sizes of the four sets A, B, C, D…

Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: Oa. Every infinite subset of Ris countable.

A:

Q: The notions of decidability and effective enumerability are applicable not only to sets of…

A: To prove the statement, we need to show both directions of the "if and only if" statement: 1. If set…

Q: Prove that the following 2 sets are equal: {4k + 5 : k ∈ Z} = {4k + 1 : k ∈ Z}.

A: Two sets are equal if and only if They have the same element  We are using here if x €A. <=>…

Q: Answer the following. Round your answers to the nearest thousandths. (a) From these results, compute…

A: outcome 0 `1 2 3 4 5 6 7 8 9 Number of trials 19 10 13 9 14 15 18 19 13 20 To Find: a) Compute…

Q: Let A = ({0} ∪ {x | x ∈ ℤ+and x < 4}), B = {0, 1, 3, 5, 7}, and C = ({0} ∪{x | x ∈ ℤ+and x is even…

A: Since you have posted a multi subparts question according to guildlines I will solve first(a,b,c)…

Q: Write a proof for the General Multiplication Principle: Suppose that A , A2, ..., An are inite sets.…

A:

Q: the universal set be the set ? of all real numbers and let A= {x ∈ R |0 <x  ≤ 2}, B= {X ∈ R |1 ≤ x <…

A:

Q: Let U= {x|x is a positive integer and x <10} be the universal set, A = {x|x €U and x is a factor of…

A: A={1,2,3,4,6} B={2,4,6,8,10}

Q: Let A = {2, 4, 6, 8, 9}. List the complete set for each of the following: V = {n+4|n ∈ A }

A:

Q: Suppose A is a set for which |A| = 12. How many 5-element subsets of A are %3D there? (the number of…

A: Here given   A is set for which |A| = 12  So here no of elements in set A = 12

Q: I=(a +1,b2, c←0, y4, z5, f←fi(d)= d+ 2, gi(di, d2) = 2(di + d2), p← pi(dı, dz, d3): d₁ + d2 <2d3, q←…

A: Given interpretation  over the domain  the set of all integers: not equal to }Objective: Expand the…

Q: Determine whether each of these sets is finite, countably infinite, or uncountable. For those that…

A:

Q: Are the following sets equal?  A = {x ∈ Z : 5 < x < 10} and B = {9,8,7,6}, where Z denotes the set…

A:

Q: Write a proof for the General Multiplication Principle: Suppose that Aq, A2, ... , An are finite…

A: Consider the given ; A1,A2,A3,A4,......,An  are finite sets.

Q: Fill in the boxes in the following proof by contradiction that: For all sets A and B, if B ⊆ A'…

A: For all sets A and B, if B ⊆ A' then A ∩ B = Ø