What will be the cartesian product of three sets if one set of them is empty?

Q: How many ways are there to paint the 10 identical rooms in a hotel with five colors if at most three…

A: Since the 10 rooms are identical, we'll ignore ordering. There are 4 places to put the divider for…

Q: Show that the set S = {(1, 2, 3), (0, 1, 2), (−2, 0, 1)} spans R3.

A:

Q: What is a set?

A: Definition of the set:

Q: What is an example of two equivalent sets with the same cardinality BUT DO NOT HAVE a one-to-one…

A: Take A as, 1,2,3 and B as 3,4,5 The cardinality of A and B is 3. Now let's define a function.

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: {(x,a),(x,b),(x,c), (y,a),(y,b),(y,c)} is the Cartesian product AXB of two sets given as A = {x,y} B…

A: Let A and B are two sets. Cartesian product of A and B will be denoted by  A×B                A×B…

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: Write out the indicated sets by listing their elements between braces

A:

Q: Provide 2 examples of sets with |A| = 4, |B| = 3, |AUB| = 6

A: Number of elements in set A is 4, in set B is 3 and in set A U B is 6.

Q: The set of elements common to both set A and set B is called ----------------- the of sets A and B,…

A: Sets are basically a collection of well defined and distinct objects. These objects can be anything,…

Q: What is meant by Intersection of sets?

A: Let A and B be the two sets. Then the set of all common elements of A and B is called the…

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

A: To check the statement

Q: What can you say about the sets A and B if A ⊕ B = A?

A: The symmetric relation is described as, A ⊕ B =(A-B) U (B-A)

Q: If A, B,C, and D are sets, does it follow that (A ⊕ B) ⊕ (C ⊕ D) = (A ⊕ C) ⊕ (B ⊕ D)?

A: The symmetric difference between the set is associative and commutative. So, (A⊕B) ⊕C=A⊕(B⊕C)…

Q: If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements andY has 15 elements ; how…

A:

Q: In a Venn diagram, the overlap of two circles represents the difference between the numbers of…

A: Venn diagram

Q: Show that each pair of sets is equivalent by using a one to one correspondence. {1,2,3,4,. . . .} is…

A:

Q: What is a set? What is a subset? How can we show that a set is equal to another set, using this…

A: To define: the set, subset. To show: a set is equal to another set. Please post the multiple…

Q: display that if A is an infinite set, then whenever B is a set, A ∪ B is also an infinite set.

A:

Q: The set of elements that are members of set A or set B or of both sets is called the. of sets A and…

A: Note that, a set is a collection of objects. All the object that are clearly determined in a set are…

Q: What is meant by the Cardinality of a finite set? Give one example.

A: The cardinality of a set is meant by the number of elements of the given set. If the set has no…

Q: The boundary of a set is equal to the boundary of the complement) True or false

A: (The boundary of a set is equal to the boundary of the complement) True or false

Q: What can you say about the sets A and B if (An B') = {}

A:

Q: Find two different sets of coins that each make 120% of a dollar, where no type of coin is in both…

A:

Q: Which sets are compact? The union of [0, 1] and [2, 3]

A: Concepts introduction: Theorem (Heine-Borel Theorem): A subset S of R is compact if and only if S is…

Q: Find the intersection of the sets. {1, 2, 3, 4} ∩ {2, 4, 5}

A:

Q: What is the size of the union of the sets A and B, if |A|=|B|=12 and |ATT B|=10?

A: The sets A and B,A=B=12 and A∩B=10

Q: Prove: The Cartesian product of countable sets is countable.

A:

Q: What is the cartesian product of sets {1,3,4} and {2,9}?

A: 1, 3, 4  and 2, 9

Q: Let A = {1,2, 3} be a set. Then the Cartesian product Ax A = {1,4, 9}.

A: In the given question we have to tell about the statement s.t are they true or false. (1) the given…

Q: Are the sets A_4 and A_5 compact sets? Why yes, why not? Ay = (,2] A- [1, 2] u [ 3, +]

A: See the attachment

Q: Explain the difference between set A and set B

A:

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: What is the intersection of sets {2,3,4} and {2,3,5}?

A: To find the intersection of given sets: {2,3,4} and {2,3,5} Solution: We know ,the intersection of…

Q: A universal set U with 66 elements has been partitioned into three subsets, A, B, and C. If B is 2…

A: We use the definition of the size of a set to find the number of elements in the set B. The size of…

Q: What are the basics of a set?

A: Set:A set is a collection of well-defined distinct objects. Here the objects are known as the…

Q: proper subset of another set

A: Given: a. A=1, 2, 3b. B=3, 2, 1c. C=Hello, Hi, Good Morningd. D=a,c,g,xe. E=3, 1, 2, 5, 7f. F=∅g.…

Q: It is the selection of objects from a set.

A: This is the problem of combinatorial. finite math, counting.

Q: Let A, B, and C be three sets. If A⊕C=B⊕C, show that A=B

A: Solution : Given that A,B and C are three sets. And the Direct sum of set A and C is equals to…

Q: Consider the following set. {-5, -4, -3,0.1. V2,2, 2.5, 4, 아 0, 1, V2, 2, 2.5, 4,

A:

Q: Do you think the set of all human beings and the set of all possible GPS coordinates have the same…

A: Both have the cardinality but not same cardinality  Cardinality is  refers to the relationship…

Q: 4.3 Give an example to show that the arbitrary intersection of open sets is not an open set.

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

Q: {(x,a), (x,b), (x,c), (y,a), (y,b),(y,c)} is the Cartesian product AXB of two sets given as

A: Given,          x,a,x,b,x,c,y,a,y,b,y,c is the Cartesian product of A×B.

Q: Determine whether each of the following statements is true or false, and explain why.The number of…

A: Let A and B be two non-empty sets. Number of elements in set A = m Number of elements in set B = n…

Q: If A and B are two sets satisfying A∖B=B∖A what can we conclude about A and B? Explain.

A:

Q: is The set

A:

Q: Question 2: Use set builder notations to prove that: a)X Y = (XUY) – (XnY), b)(Y – X) U (Z – X) = (Y…

A: Part(a) We have  by the definition of symmetric difference : X⊕Y=xx∈X-Y or x∈Y-X Now, we prove that…

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

A: Here use definition of complement of set

Q: The symmetric difference of two sets A O B is the set of elements that are in either the set A, or…

A: The aim is to show that, A⊕(B⊕C)=(A⊕B)⊕C It is known that, A⊕B=A∪B-A∩B So A⊕(B⊕C) can be written as,…

Q: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C. If B is 4…

A: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.