Question from Discrete Mathematics: Let a and b be two elements in a lattice (A, ≤). Show that a ˄ b ˂ a and a ˄ b ˂ b if and only if a and b are incomparable.

Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are %3D %3D two sets. find R = {(x, y): x E X and y E Y…

A: There are only three pairs of elements which are satisfied the given conditions

Q: Define the partially ordered set (N",<) as follows: x < y if Xi < Yi for all 1<i<n. For example, (2,…

A:

Q: ) (AO B) © (A^ B) = A UB.

A: Introduction :

Q: 9. If (X, M, ) is a measure space and E, FEM, then μ(E)+μ(F) = μ(EUF)+ μ(EnF).

A:

Q: If C = {x:x² + 11x + 30 = 0,x E N}, then C is a/an? Finite set None of these Empty set Infinite set

A: A set which contains no element is called null set or empty set.  A set S is said to be a finite set…

Q: 2.5.22. Let A, B,C be three sets. Prove that if A \ B C C, then A \C C B.

A: Given: Let A,B,C be the three sets. A-B contained in C

Q: a) Proof that for each set A, A = A n A. b) If A and B are subsets of S, simplify (A U B) n (A' U B)…

A: Any subset of the sample space of a random experiment is called an event and is denoted by capital…

Q: 12. Let B be a subset of A. Let |A| = n and |B| = k. What is the number of subsets of A whose…

A: Given B⊂A. A=n and B=k Now if any subset C of A has 3 elements in intersection with B then C≥3 For…

Q: Let A and B each be sets of N labeled as vertices, and consider the bipartite between A and B 1. How…

A: Given: There is two sets A and B of N labeled as Vertices.

Q: Proposition 1.43. A is the intersection of all closed subsets of X which con- tains A. Proof.…

A:

Q: A set D C RP is disconnected if and only if D = EU F, where E, F are non-empty and EnF= ø,EnF = Ø.

A:

Q: Roster form: C = { Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday } What is the Set…

A: To change  roster form to set builder form

Q: Let (D30, ) denote the poset of all divisors of 30. a. Show that D30 is a lattice. Explain. b. Is…

A: Let &lt; D30, | &gt; denotes the poset of all divisors of 30

Q: Exercise 5.2 | Show complete proof/solution. Let r > 0 and x E R". Show that the following set is…

A:

Q: (a) Prove the following statement using the element method for proving that a set equals the empty…

A: (a) Suppose that A and B are two sets. It is known that, B-A represents the set of elements in B…

Q: a). Define pandent vertex and isolated vertex by giving example.

A: As per our company guidelines we supposed to answer only first question. kindly repost another in…

Q: Exercise 2. Let A, B C R. (a) Prove that AUB = AUB. (b) Prove that ANBCAN B. (c) Find sets A and B…

A: Solution:-

Q: 1) Prove that AU(Bnc)= (AUC)N(AUC) 2)Let M-{1,3,n}, find the power set of set M

A: Find the attachment

Q: How many permutations of the set {1,2,3,4} do not correspond to symmetries of the rectangle? Justify…

A: Suppose the vertices of a rectangle are denoted by the numbers 1, 2, 3, and 4. Then, we have four…

Q: We know that P₁ = P2 on B if P₁ = P2 on C, provided that C generates B and is a 7-system. Show this…

A:

Q: 2. Show using Venn diagrams the following are true: a) (A – B) C A b) An(B – A) = Ø

A:

Q: (iv) Prove that for any sets A, B,C we have A U (B nc) = (AU B)n (AUC)

A: To prove:- Prove that for any sets A, B, C we have AU (B∩C) = (AUB)  ∩(AUC) Method :- I use venn…

Q: 9. If (X, M, u) is a measure space and E, FEM, then u(E)+μ(F) = μ(EUF)+ μ(EnF).

A: Introduction: A measurable function is a function between the underlying sets of two measurable…

Q: Consider the set S = {zeC:0< Re(z) < 2 & 0<Im(z) < 3} What is its interior? {zeC:0<Re(z) < 2 & 0<…

A:

Q: 2. Let A, B, and C be sets. with (A - B)nC the empty set. Prove that AnC C B.

A: Recall the following. A-B=A∩BcIf x∈A⇒x∈B, then A⊂B

Q: Proposition 2.18. Let (X,T) be a topological space : (1) (A°)° = A°. (2) ACB⇒ A° C B° for all A, B €…

A: The interior of a set is the union of all its open subsets interior point A point in a set that has…

Q: Exercise 1. Prove that for sets A, B,C we have C \(AUB) = (C\ A) N (C \ B).

A: We have to show that for sets A, B, C   C ∖(A∪B)=(C∖A)∩(C∖B).

Q: Q. Let N = (1.2, 3...) equipped with the cofinite topology. If M = (3k, k e N} = [3,6,9, 12,..},…

A:

Q: Proposition 1.36. For any metric space X, the empty set o and the whole set X are closed in X.…

A: For any metric space X, the empty set ϕ and the whole set are closed in X

Q: Let Ak = [k – 1, k] and Bg = [k, k + 1] Find the set U0 (Ak N AK)

A:

Q: Show that a lattice is distributed if and only if for any elements a, b, c in the lattice (avb)^с ≤…

A: To Show- Show that a lattice is distributed if and only if for any elements a, b, c in the lattice a…

Q: Find sets A, B and C such that A ∩ B,    B ∩ C and A ∩ C are non-emptysets and A ∩ B ∩ C = φ.

A:

Q: 3. Let A, B, and C be sets. Prove or disprove that A- (BNC) = (A-B) U (A-C).

A: Solution

Q: For what values of n does Kn have an Euler circuit? Explain.

A:

Q: d) The set E = (-1,0) U (0, 1] is an open set. %3D

A: Given set is E = (-1, 0) ∪ (0, 1]

Q: If C {x: x2 + 11x + 30 0, x e N}, then C is a/an? %3D Infinite set Finite set None of these Empty…

A: We have to find the set C

Q: Let X = {a, b, c, d, e} and let T= {X, Ø, {a), {c,d}, {a,c,d}, {b,c,d,e} }, then O X T) is neither…

A:

Q: for fuzzy sets A, B and C, (AVB)vc = AVIB VC). (Ал в) лс - АЛ(ВЛС). (A V BF = A“AR prove that AA CB…

A:

Q: Let A = {small, medium, large}, B = {red, black}, and C = {pentagonal, round}. List the elements of…

A: Given : A =small, medium, largeB = red, blackC = pentagonal, round

Q: Consider following five sets: I. { , } { } II. { } III. IV. { , , } V. { , } Find all linearly…

A: We have to check whether given set of vectors linearly independent or linearly dependent by known…

Q: 5. Let (X, B(R), µ) be a Borel measure space. Suppose that {A,, = ["+1, 4n-1]}" be a family of…

A:

Q: Let S = {-4,-1,0,2/3,5/6,1,√5,3,5} determine which elements of S satisfy the inequality -2+3x ≥ 1/3

A:

Q: Proposition 1.36. For any metric space X, the empty set o and the whole set X are closed in X.

A: 1. Let X be a metric space with metric d. If is a point of X and r is a positive real number, the…

Q: Write a paragraph that explains why the following proposition is false (Hint: draw a picture and use…

A: Given that A, B, and C are three non colinear points. So the points A, B, and C not lie on the same…

Q: 3. Let A, B, C, and D be sets. (a) Prove that (A × C) n (B × D) = (An B) × (Cn D).

A: Let A, B, C, and D be sets.To prove the equality, we have to show that, LHS is a subset of RHS and…

Q: Let A and B be sets. Prove that A UB= (A – B) U (B – A) U (A N B).

A:

Q: A={ z ∣ z ∈ N and 195 ≤ z ≤ 201} Use the roster method to list the elements in the set A. A=

A: Given: A={ z ∣ z ∈ N and 195 ≤ z ≤ 201} The roster form is given by

Q: Give an example of an infinite lattice with a) neither a least nor a greatest element. b) a least…

A: Given :- An infinite lattice with  (a) neither a least nor a greatest element (b) a least but not a…

Q: 3. Consider three finite sets A, B and C. Show that: (a) (b) (c) (AB) x C = (A ×C) \ (B × C ); (AUB)…

A:

Q: 3A, B E {sets} such that A CBAA= B.

A: To check whether the given statement true or false: ∃A,B∈sets such that A⊆B∧A=B