5. Give an example (by words) for a collection of objects which is not well defined

Q: 2. Finite subsets of Rd are closed. Gap to fill in

A: Given statement is Finite subsets of ℝd are closed.

Q: if A ={x,{y},1,2,3,{2,3},{3}}      {} a proper subset of A      true or false

A: The problem is concerned with the nature of the empty set. The specific question is whether the…

Q: Problem 5. Give an example to prove that the union of infante closed sets is not necessarily closed.

A:

Q: Explain the main difference between Julia set and a Mandelbrot set.

A: We know that, For a complex numbers c, Both Julia set and Mandelbrot set of c is the set of all z…

Q: Suppose that |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2. Determine the smallest that |A…

A: Given, |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2

Q: 8. Disprove that every compact set has only a finite number of isolated points. V Note that the…

A: Let C be the compact set.If possible suppose that 'C' has a infinitely many isolated points. say…

Q: True or False The intersection of two sets is always a subsetof their union

A: To check the statement

Q: 4. (10 points) Show that if A is an infinite set, then whenever B is a set, AUB is also an infinite…

A:

Q: find a set of smallest possible size that has both {3,4,7,8} and {1,5,6,9,10}

A:

Q: a) If there are no two donuts of the same variety b) If there is no restriction c) If there must be…

A:

Q: A. Compute the total number of sets (of size 5) containing exactly 2 elements from X and 3 elements…

A:

Q: How many subsets with an odd number of elements does a set with 12 elements have?

A: Given that a set contains 12 elements. We need to calculate the total number of subset with an odd…

Q: What is the minimum number of students required in a discrete mathematics class to be sure that at…

A: We solve the given problem in next step.

Q: 2. (i) Show that given finitely many countable sets A1, A2, , An, the set A1 x A2 x .. x An is also…

A:

Q: what are subsets?

A: Let us consider two sets A and B.A is called subset of B if and only if B set have all elements of A…

Q: 4) Suppose there

A: Given, there are a million cars made by a car company across the globe, where the probability that a…

Q: 6.3.16 How many subsets with an odd number of elements does a set with 10 elements have?

A: Consider that the set has 10 elements and we need to find the subsets with an odd number of…

Q: Calculate the number of subsets and the number of proper subsets for the given set. {x|x€N and…

A:

Q: Consider the set X = {A,B, C, D,E, F, G} case 1 How many 4-letter lists from X (with repetition…

A: A set X is given. We have to find the number of 4 - letter lists possible from X if certain…

Q: Suppose we want to choose 6 objects, without replacement, from 10 distinct objects. (a) How many…

A: We can find answer to both the question as below

Q: A(n) _____ is a collection of items called elements

A:

Q: 8. Show that the set (0, 1) – {1/2, 1/3, 1/4, -..} is uncountable.

A:

Q: 8. (a) Show that the intersection of finitely many open sets is open.

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose that A = {2,4,6}, B={2,6}, C = {6,8}, and D = {4,6,8}. Determine which of these sets are…

A: given sets are A =2,4,6 B = {2,6} C = {6,8} D = {4,6,8}

Q: If A (5, 7, 8, 9}, B = {3, 4, 5, 6} and C = {2, 4, 6, 8, 10}; where n is total number of distinct…

A:

Q: What is the minimum number of cards that must be drawn from an ordinary deck of cards (52) to…

A: Given problem Given that   The minimum number of cards that must be drawn from a ordinary deck of…

Q: How many subsets does the set  F = {3, 4, 5, 6, 7} have?

A: No. of subsets in a set: The number of subsets in a set containing n elements is given by 2n. No. of…

Q: Find a set of smallest possible size that has both {3,4,7,8} and {1,5,6,9,10} as subsets.

A:

Q: If G(sub alpha) is a collection of closed sets, then the intersections of the G(sub alphas) is a…

A:

Q: Suppose we want to choose 5 objects, without replacement, from 18 distinct objects. a) If the order…

A: Given,Total no.of distinct objects=18

Q: 11. Discuss briefly using significant word why it might be difficult to describe "a collection of…

A: Given that: 11. A collection of numbers.   NOTE: As per our answering guidelines, we can only answer…

Q: Discuss the important characteristic that a counting problem has to have in order to classify it as…

A:

Q: 5. Show that a finite union of countable sets is countable.

A: The answer is given as follows :

Q: How many subsets of a set with 64 elements have more than two elements

A:

Q: Suppose that there are 27 students in discrete mathematics class. Show that the class must have at…

A: Here we solve this question by contradiction.

Q: How many unordered sets are there of two items chosen from eight?

A: To find unordered sets of two items chosen from eight. Number of unordered sets r chosen from n is…

Q: Construct an intersection graph of this collection of sets. A1 = {0, 2, 4, 6}, A2 = {0, 1, 2, 3, 4},…

A: We have to construct an intersection graph of collection of sets. A1 = {0, 2, 4, 6}, A2 = {0, 1, 2,…

Q: Suppose we want to choose 6 objects, without replacement, from 9 distinct objects. (a) If the order…

A: Solve

Q: 7. Show that the Obenchain class LOb(B) is a convex set.

A: Given: To show the Obenchain class LOb (β) is a convex set is given as,

Q: If 1/3 of the blocks in set A are red, and 1/4 of the blocks in set B are red, does it follow that…

A: Given 1/3 of blocks in set A are red and 1/4 of blocks in set B are  red

Q: 5. Show that a finite set is a closed set.

A:

Q: What is the minimum number of students required in a discrete structures class to be sure that at…

A: As we have five grades: k=5 And the number of students: r=9 And we have to calculate: Nk=r N5=9

Q: Suppose we want to choose 5 objects, without replacement, from 15 distinct objects.

A: Given data: The total numbers of objects are n=15. The numbers of objects choose is r=5. (a) Write…

Q: 2. Show that the set N has no limit point.

A:

Q: how that the union of a finite. number of bounded sets is bounded

A: A statement is given as, 'the union of a finite number of bounded sets is bounded. The objective is…

Q: se the roster method to write the set A'.

A: Here use definition of complement of set

Q: prove that every subset of negligible. set is negligible.

A: I have used definition of negligible set.

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.