et A = {2,3,4, 7, 19, 21} and define < on A by x < y if and only if (y – 1)|(x – 1). a. Show that (A, 3) is a poset. b. Draw the Hasse Diagram of the poset. c. Find any maximal and minimal element/s. d. Find any greatest and least element/s. e. Find all lower bounds and all upper bounds of {4, 7}. f. Find the glb({4,7}), if it exists. -

Q: Prove or give a counterexample to the following statement: for any relation R both R and RoR always…

A: Suppose R is a relation on a set X, then the transitive closure of the relation R is the smallest…

Q: 14. Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A→ B as follows: For all (x, y)…

A:

Q: Draw Hasse graph of partially ordered set (A,), where A=(1), (2) and (4) 2), (1, 4), (2, 4), (3, 4),…

A:

Q: this question and subsequently, let a₁, A2,..., a5 denote these numbers: 2,2,1,7,3 Let X denote the…

A:

Q: Show that For n > 1 let G, be the simple graph with vertex set V(Gn) = {1,2,., n} in which two…

A: A simple connected graph G is said to be planar if we can draw the graph in the plane with no two…

Q: Let RC RX R with {(x, y) |x² =5 y²}. Characterize R in terms of whether it is reflexive,…

A: A reflexive, symmetric, transitive binary relation on a set is an equivalence relation. In other…

Q: Let (A= (2, 4, 6, 9, 12, 18, 27, 36, 48, 60, 72), R) be a partially ordered set, where the relation…

A: We have to find the smaller element of set. Set of all upper and lower bound.

Q: 1. Let f = {(1, 2), (3, 4), (2, 6), (5, 9}. a) Find the domain of f: {1, 2, 3, 4, 5} O {2, 4, 6, 9}…

A:

Q: a. xRy x C y

A: Since you have asked multiple question, we can solve first question for you. If you want other…

Q: 1. (10 points) Consider the set 2020n + 2021 S = :n = 1,2, 3, n+1 Find sup(S) and inf(S) and…

A: Since you have asked multiple questions, we will answer the first one. If you want other questions…

Q: 1. Complete each statement for the translation T:(x, y) → (x + 3, y - 1). a. T glides points units…

A: T:(x,y)→(x+3 , y-1)

Q: Let Ω-set of all real numbers, A-index set. Identify the generalized union and intersection of the…

A: Given: Ω set of all real numbers To find: Solution

Q: Direction: Define subsets of Za, as follows: A = {a | a E Za and a 5} A = {a | a E Za and 3| a} 1.…

A:

Q: Find the closure of each of the following sets: (a) (3,5) U {6} (b) (-∞, 0) U (0, 1)

A:

Q: 3. Use function f(x) = *** to show that Card(R – {5}) = Card(R – {1}) step by step. (Note: Card(A)…

A:

Q: 4. Determine which properties (reflexive, irreflexive, symmetric, antisymmetric, transitive) does…

A:

Q: 1. Let X-(a,b,c} and T X={Ø,X,{a},{b},{a,B}}, (i) Write down all open subsets of X. (ii) Write down…

A: If (X,T_X) is a topological space. Then elements of T_X is called open sets and a set is closed if…

Q: 1. (a) Let A = {k, k +1,..., k2}, for k = 1,2,3,.... Uº1 Ak - n=1 Ak (b) Find two infinite sets A…

A: Part (a):- Given that  Ak =  k, k+1, ......, k2 ,   for  k=1, 2, 3,....Find    ∪k=150 Ak - ∩k=1∞ Ak…

Q: (b) Let V = {0, 1, 2, 3,..., 13}. Draw the graph G = (V, E) where {s, t} € E if and only if 7 | (s –…

A: The vertex set is: V=0, 1, 2, 3, …, 13 The graph G=V, E has the property that s, t∈E if and only if…

Q: O let fu be the function graphed below aFind the domaln of of 7. 91 b. Find the rongecoff t200 a CA…

A: Given, Let f(x) be the function of the graph below,

Q: Let An denote the number of lattice paths from (0,0) to (n, n) that do not pass above the diagonal y…

A: As per the norms, we will be answering the first question. If you need an answer to others, then…

Q: For each of the following relations on a set {1, 2,3,4}, decide whether it is reflexive, whether it…

A:

Q: 4. Define a relation R on N by aRb if a and b have no common factors except 1. (a) Give an example…

A: We have define  a relation R on natural numbers (N) by aRb if a and b have no common  factors except…

Q: 1. Let R be the relation on N defined by "aRb if EN or 5| (b- a)". So for example (6, 2) € R and…

A:

Q: 6. (a) Let sets S = {A, B} × {1, 2, 3} and T = {A, B} × {1, 2, 3, 4} . How many different one %3| to…

A: The total number of elment in set s will be  and total number of element in set T will be

Q: 2. Let S = {0, 1, 2, 3, 4} and T = {0, 2, 4). (a) How many ordered pairs are in S × T? T × S? (b)…

A: 12. Given that,                    S=0, 1, 2, 3, 4  &amp; T=0, 2, 4.

Q: 2. Answer the questions with Yes or No, and then explain why yes or why not. Justify your answer. a)…

A: Answer :

Q: 4. (5 points) Find a counterexample to show that the following statement is -3 false. For all sets A…

A:

Q: 1- show that [Am, A¹] = 0 for all m and n discuss the physical meanings of this relation. 2-…

A: As per the question we are given the following commutation operations : [Am , An] [∂/∂x , x] And…

Q: (2.1) Let b> 0 and X [-b, b). Here we admit %3D B"open" in r if and only if (0} B or (-b, b) C B.…

A:

Q: Which of the following sets is not closed for the operation °, which is defined by the rule a°b = a…

A: Option (a) is not closed under the operation °.Option (b), (c), and (d) are closed under the…