Let A and B be two sets with a finite number of elements. Show that the number of elements in An B plus the number of elements in AU B is equal to the number of elements in A plus the number of elements in B.

Q: The set having elements of the complement of the set A will be,

A: We need to find out complement of A.

Q: Let 4, B, and C be sets. Show that а) (А — В) — С СA-C. b) (A — C) n (С- В) — 0.

A: It can be solved by the set theory

Q: Let A and B be subsets of a universal set U and suppose n(U) = 300, n(A) = 150, n(B) = 120, and n(A…

A: Please see the below explanation.

Q: Prove that if A and B are transitive sets, then A ∪ B and A ∩ B are transitive sets

A:

Q: Let set A be the set of face cards and B be the set of all spades in a regular deck of cards. State…

A: There are 12 face cards in a regular deck of cards and 13 spades in a regular deck of cards. Set A:…

Q: Suppose A, B and C are sets. Prove that if A ⊆ B, then A - C ⊇ B - C

A: Dear student in the question we can't prove,  Suppose A, B and C are sets. Prove that if A ⊆ B, then…

Q: Suppose that A and B are finite sets. Prove that A U B is finite, and |A U B| = |A| +|B| -|A n B|.…

A:

Q: Suppose that A and B are sets. Prove that A- B = AnB.

A: Suppose that A and B are set. Prove that A-B=A∩B¯.

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

A:

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

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

Q: Suppose A and B are finite sets. Prove or disprove: (aun-aun)- (AUB) = (A u B) ) + Dsjnt(A, B)

A: Consider the equation

Q: . Let A and B be two connected subset

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

Q: Let A and B be subsets of a universal set U and suppose n (U) = 275, n(A) 100, п (В) = 70, п (An B)…

A: If A is subset of universal set U, then n( Ac ) =n(U)-n(A).

Q: For an element to be in the intersection of sets A and B, the element must be in set Am in set B.…

A: Any elements of A intersection B must be in set A and in set B

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

A:

Q: 6. Let A, B be finite sets. Show that if JA\ B| = |B\ AJ, then |A| = |B|.

A: The order of a set defines the number of elements of the set. For two finite sets A and B,…

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

A: Let A, B and C are sets. We have to find out that A-B = A- C implies B = C or not If not then we…

Q: 4. Let A and B be sets, prove that P(A)UP(B) C P(AUB).

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: 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: Let A, B, and C be sets. Show that (A-B)-C=(A-C)-(B -C).

A: A, B, C are any set, we need to show that (A-B) - C = (A-B) - (A-C) this can be done using the…

Q: Let U be the set of restaurants in Los Angeles, B be the set of barbecue restaurants in Los Angeles,…

A: Given Information -  U is the set of all restaurants in Los Angeles B is the set of barbecue…

Q: Let the Universal Set, S, have 78 elements. A and Bare subsets of S. Set A contains 44 elements and…

A: Given data: The numbers of elements in the universal set are n(S)=78. The numbers of elements in the…

Q: Use the element method for proving a set equals the empty set to prove that: For any A, B sets, (An…

A: Since you have post multiple question I only solve first one.

Q: Let A = {a,b,c,d} be the set containing the four elements a, b, c and d. Let S = {X |X is a subset…

A: Sets

Q: Let A and Bbe finite sets satisfying |A|= 9, B| = 6 and |An B = 2. Calculate the following: () |AUB…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Let A, B and C be three sets. If A ∈ B and B ⊂ C, is it true that A ⊂ C?. If not, give an example.

A: No, it is not true. EXAMPLE- Let A= {2}  B= {{2},3,4} C={{2},3,4,5,6} We can see here that,

Q: The empty set is open set ylgn O İhi O

A: The complement of an empty set is the whole set, which of course contains everything including all…

Q: If A is a countable set and B is a subset of A then

A: If A is a countable set and B is a subset of A then B is also a countable set since, every subset of…

Q: Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, find n(A ∩ B).…

A:

Q: let X={a,b,c} Construct two topologies for the set that have at least 4 open and that are…

A: Given that X=a,b,c. To construct two topologies that have at least four open sets. We know that in…

Q: For any sets A  B, C, ( A ∩ B) ∪ C ≠ A ∩ ( B

A: Given that the sets A, B, C. Consider, A∩B∪C=A∪C∩B∪C.............(1) Consider,…

Q: Let A, B and D be sets. If A n B = Ø then prove that (A – B) – (B n D) = A.

A: Take x in left hand side and prove it belong to A and vice versa.

Q: For any sets A and B, (AUB) = A' NB'.

A: For any two sets 'A' and 'B' A∪B'=A'∩B' In order to prove equality we will show: (A∪B)'⊂A'∩B'…

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: If a set A has 5 elements, then the total number of possible relations on A is 255 252 25 52

A: Given below the detailed solution.

Q: for any sets A and B (AUB)'=A'nB'

A: We prove that for any sets A and B (AUB)'=A'nB'.

Q: Show that if A and B are finite sets, then A ∪ B is a finite set.

A:

Q: Let A, B, C be three sets. Show that if B C A and C C A \ B, then BC A \C.

A: Given: Let A, B, C be three sets. To show: If B⊆A and C⊆A \ B, then B⊆A \ C.

Q: Prove that if A ~ B then P(A) ~ P(B).

A: Consider the provided question,

Q: Let A, B be any sets with BCA. Then |P(B×B)[s|P(A×B)| O IP(AxB)|s|P(B×B)| O IP(AxB)|=|P(B×B)| O None…

A:

Q: Let A, B and C be finite sets with A C B. Suppose that B |C| =5, and that |BnC= 4. Decide whether…

A: Given: A⊂-B, |B| = |C| = 5 and | B∩C| = 4

Q: Let at AuB = {1, 2, 3, 5, 8}, Cc = {4, 7, 9} and let the universal set U be all positive integer…

A: From the information, AuB = {1, 2, 3, 5, 8}, Cc = {4, 7, 9}, U={all positive integer less than or…

Q: Show that the union of two sets, each of measure zero, has measure zero

A:

Q: Let A and B be sets. Define precisely (but concisely) what it means for A to be a subset of B

A: Let, A and B be setswhat it means for A to be a subset of B.

Q: let sets a and b be defined as follows. A is the set of integers than or equal -5 and less than or…

A: Solution: Let sets A and B A={the set of integers greater than or equal -5 and less than or equal to…

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”.