Show that if A is an infinite set, then whenever B is a set, AUB is also an infinite set.

Q: Provide a counterexample for the statement: For any sets A,B and C, А - (В -С) — (А - В) — С.

A:

Q: If the number of elements in a set is a nonnegative integer,we say that the set is_______

A: Finite sets- A set with finite number of elements is known as finite set. The number of elements in…

Q: The interval [0, o∞) can be expressed as A. n (an, 0) where each an is a rational number B. U(an,…

A: (a) To show ∩n=1∞an,∞=[0,∞), where each an is rational number. Since we are considering intersection…

Q: Express the following set in set-builder notation. B= {14, 15, 16, 17, 18, 19, 20, 21} Choose the…

A:

Q: The qualifying time to make it into the 5K race is 20 minutes or under. Which inequality statement…

A: Explanation of the answer is as follows

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: a. With no restrictions b. If each couple is to sit together? c. If all the men sit together to the…

A:

Q: Define E to be the empty set and further define F = {E}, G = {F}, H = {E, F}, and I = {E, F, G,H}.…

A:

Q: Select the reason that best supports Statement 8 in the given proof. A. Addition Property of…

A: Our Aim is to select the reason that best supports Statement-8 in the given proof.

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: Show An(B-C) = (AnB) - (ANC) using set operations and identities.

A:

Q: If either A or B empty set then Ax B equal empty O A

A: The solution is given as

Q: Đ A is a closed set.

A:

Q: Use the formula for the cardinal number of the union of two sets to solve the problem. set A…

A:

Q: Use the rule method to describe the following sets. 1. The set Z of negative integers greater than…

A: 1. Given: The set Z of negative integers greater than -6 To find the following statement using in…

Q: Prove if the following statement is true or disprove if it is false. If A and B are finite sets,…

A:

Q: Is it true that for any sets A and B,        P ( A ) ∪ P ( B ) = P ( A ∪ B )? Justify your answer.

A:

Q: Identify the set theory /logic expressions from looking at a shaded Venn Diagram attached.  Please…

A: In the given figure it can be observed that the colored space is the collection of elements that are…

Q: In Section 6.2, there is a list of set identities. As you go through the list, you will recognize…

A:

Q: Which of the following sets is a universal set for the other four sets? O The set of even natural…

A: .

Q: The transitive property of equality states that if AB = BA, then BA = AB. %3D %3D O True O False

A:

Q: a) Prove that the set { 1} is an adequate set of connectives. b) As a result of a) above or…

A: Given: The statement form is ¬P→Q∧¬R

Q: 8. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A: Define A={1,2} and B={1}.

Q: 18. There is a set X for which Ne X and NsX.

A: As N is set of natural numbers , so  for N to be subset of X and N belongs to X , we can consider X…

Q: Prove for every two sets A and B that A∪B= (A-B)∪(B-A)∪(A∩B)

A:

Q: Answer the questions with Yes or No, and then explain why yes or why not. Justify your answer. Does…

A: The equality A∪B=A+B is not always true for every sets A and B. It is true only when A and B are…

Q: - Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A:

Q: 5. Given sets A and B, define their symmetric difference as AAB = (A – B) U (B – A). Use the set…

A:

Q: The symbol Ø refers to the empty set. What is the cardinal number of the empty set?

A:

Q: When using Venn diagrams to verify or determine whether set statements are equal we use…

A: Deductive reasoning, also deductive logic, is the process of reasoning from one or more statements…

Q: Give a counterexample to show that the statement For all sets A, B and C, if A⊈BandB⊈C,thenA⊈C.…

A:

Q: 5. Given sets A and B, define their symmetric difference as AAB = (A – B) U (B – A). Use the set…

A:

Q: How to Apply the Archimedes'principle to prove that a set is empty

A: Consider the given information. the Archimedes' principle is defined as, Property states that for…

Q: Determine if the following statements are true or false.

A: We have to identify the given statement as true or false.

Q: Write the interval in set-builder notation. [-4, 1] U [5, ∞0) O {xl-52 x ≥ 1 orx ≤ 4} O {x|-4 ≤ x ≤…

A: Set builder notation is represented as Interval notation, and it is a way to define a set of numbers…

Q: Refer to the accompanying figure, and list the points that belong to each set. (Enter your answer…

A: A = {r, u, v ,y} B = {r, v, w, x} C = {r, u, w, z}

Q: Give a proof by contradiction to show if C and D are sets, then C ∩ (D ∩ C’) = {}.

A: Given C and D are sets.

Q: Is A countable or uncountable?

A: This is a problem of real numbers properties of topology.

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: Give five examples of Venn diagram 3 sets with problem solving-and solution

A: Venn diagram is used to solve mathematics expressions like sets, union, intersection. Venn diagram…

Q: Write the following S= {0, 1, 2, …, 10} in set-builder notation using x as the number of integers in…

A: Set builder form: It is used to express or describe a set, it is a mathematical shorthand for…

Q: If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements,…

A: Given that n(X ∪ Y)= 50  n(X)= 28 and n(Y)=32  We have to find n(X ∩ Y )= ?

Q: Provide a counterexample to show that each statement is false. You may use words or a diagram. If ab…

A:

Q: Two sets are said to be disjoint if their intersection is zero. Select one: O True O False

A:

Q: The set of numbers in the form , where a and b belong to the set in statement 7 above and b 0, is…

A: Rational number: Rational numbers represented by ab where a and b are real number and b≠0.

Q: The number of relations on the set A = {1, 2} is 256 . O True False

A: Number of relation with n elements 2n2

Q: Let A and B be finite sets with |A|=10, |B|=5, |A∪B|=12 what is |A∩B|?

A: Given,  |A|=10 |B|=5 |A∪B|=12 |A∩B|=?

Q: what does R mean in R-C=C' , is that a universal set ?

A: Here R=universal set.   The Venn diagram of C is:   The Venn diagram of R - C is: