Give a real-world example of the inclusion/exclusion principle that involves at least two finite sets. Specify values for three of the following four values: the size of the first set, the set of the second set, the size of the union and the size of the intersection. Apply the inclusion/exclusion principle to determine that value of the one value that you did not specify.

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: An architect designing a parking lot has a row 62.0 m wide to divide into spaces for compact cars…

A: We need to formulate a system of linear equations using the scenario. We also need to solve the…

Q: Give an example of each of the following or explain why you think such a set could not exist. (i) A…

A: (i). Such a set could not exist. Let  be a nonempty subset of a topological space . Let . If  is not…

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

A:

Q: 3. Find an example of two nonempty sets A and B for which A x B = Bx A is true.

A: To find an example of two nonempty sets A and B for which AXB=BXA

Q: Which of the following is the correct representation of A {2,4,8,16,32,... } in set builder…

A: To determine the correct representation of A=2, 4, 8, 16, 32, ... in set builder notation.

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: The boundary of a set is equal to the boundary of the complement True O False O

A: A point of a set is called boundary points if any neighbourhood of this point contains point of the…

Q: What is the intersection of sets A and B?

A: The intersection of sets is a set which include the common of the two sets A and B. It is…

Q: Determine whether the symmetric difference is associative; that is, if A, B, and C are sets, does it…

A: Truth table for the symmetric difference is,

Q: 4. Is the set Q² x {a,b,c} countable or uncountable? You must justify your answer with a proof.

A: Given : ℚ2×a , b ,c  To Prove : ℚ2×a , b ,c  countable or uncountable

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: you were introduced to the set operations of "union", "intersection" and "complement." Do you see a…

A: To explain the similariites between the opreations in set theory , logic and electronic circuits

Q: Let Aand B be non-empty sets such that |A|>|B|.If the number of elements in A∪Bis atmost 42 and at…

A: Let the number of elements in A is a , hence, |A|=a . Let the number of elements in B is b , hence,…

Q: Create three non-empty sets A, B, C, that show this statement is FALSE: For all sets A, B, C: A- (Bn…

A:

Q: The symmetric difference of sets A and B, consists of those elements which belong to A or B but not…

A:

Q: 4.1 Write down the identity element of the set and substantiate. 4.2 Write down the set of inverse…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for you…

Q: Write a sentence of the form “. . ⊆ . . ” involving A, B, and at least two of the operations ∪, ∩,…

A: Given: A and B are any sets. To write: Sentence of the form “. . ⊆ . .” involving A, B, and at least…

Q: Let A and B be infinite sets that are uncountable. Do an and B have the same car finality as each…

A: Let A and B be infinite sets that are uncountable. Do A and B have the same cardinality as each…

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: The empty set o is open set

A:

Q: If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10…

A:

Q: Assume that the statement applies to all sets. Is it true or false? A – (BO C) = (A – B) (A – C) 2.

A: A-(B INTERSECTION) C= (A-B)INTERSECTION(A-C)

Q: Find the interior and boundary of the set: [0, 2] n [2, 4]

A: In the given question we have to find the interior and boundary of the set [0,2]∩[2,4]. Interior…

Q: Denote the set in set-builder form {6, 12, 18, ….66}

A: The objective is to denote the set {6, 12, 18, ….66} in set-builder form.

Q: 1) Use any method(descriptive, roster method and set builder notation) to give three examples of…

A: 1) A=Set of water droplets B=Set of stars in the midnight sky. C=Set of cells in human body

Q: Find the complement of the set given that U={x xEI and -3<x<9}. (Enter your answers as a…

A:

Q: 4. Write the set in the form (x P(x)}, where P(x) is a property that describes the elements of the…

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: Provide examples of sets A and B where strict inequality sup(A+B) < sup A+ sup B holds.

A: We have to given an example to prove given inequality:

Q: What is the complement of the set X? How is it denoted?

A: Universal set is always given to find complement of a set. Complement of a set 'X': It includes…

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: Suppose A and B are two finite sets such that |B| = 2 |A| and the number of relations on A is 16.…

A:

Q: If X and Y are two sets such that X has 30 elements and X ∪ Y has 50 elements and X ∩ Y has 8…

A: We are given: X has 30 elements and X ∪ Y has 50 elements and X ∩ Y has 8 elements We need to find:…

Q: Express the following statement into a Set Builder Notation 1. (2, 4, 6, 8, 10} 2) (2, 3, 5, 7, 11}…

A: # we are entitled to solve 3 subparts. please resubmit the other parts if you wish to get it…

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: 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: 2 3 4 5 Write the set in the set-builder form.

A: Given

Q: Let A, B, and C be sets. Does A – C = B – C imply A = B? If so, prove it. If not, give a…

A: We have to give a counter example for  A – C = B – C imply A = B.

Q: Express (4, 10) as a set {x: Ix - al&lt; c} for suitable a and c.

A:

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

A: The answer is given as follows:

Q: Express the following set in set-builder notation. B=(13, 14, 15, 16, 17, 18, 19, 20)

A:

Q: 28. Which of the following sets does not have the completeness axiom? A. R {0} B. R+ C. Q {0} D. R…

A: We have to determine which sets doesn't have the completeness axiom .

Q: Give an example of two sets A and B which are homeomorphic, A is complete and B is not.

A:

Q: Make sure that the set {(-1,1), (3, 0), (2, 5)} generate R4

A:

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

A: Here use definition of complement of set

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: Determine whether the set S = {−2x + x2, 8 + x3, −x2 + x3, −4 + x2} spans P3.

A: Given a set, S=-2x+x2,8+x3,-x2+x3,-4+x2 We need to determine whether S spans P3.