6. if x C y. (a) (b) Let R = {a: a is a cut}.Let x, y, E R. We say that a

Q: Discrete math.  Let S = R. On S we define the relation R as follows (∀x)(∀y)(xRy ⇔ y ≥ x + 3). Is R…

A: The given set S=ℝ. The relation R defined in the set S is ∀x∀yxRy⇔y≥x+3. We have to check whether…

Q: Prove that P(XY) = P(X)n P(Y) for all sets X and Y.

A:

Q: 7. (10 points) Let f: A B be onto. Prove that S((C)) = C for all sets CC B.

A:

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: ) Let R = {(a,b) : 3keza = k * b} be a relation over the positive integers. Prove or disprove that R…

A: Given that R=(a,b):a=k*b To show reflexive it is enough to show that a~a. It is true because, a=1*a.…

Q: Let S be set of all strings of a's and b's. Define a relation R on S as follows: Vs, t E S, sRt e…

A: Let A be any and let R be any binary relation on the set A. Relation R is symmetric if for a, b∈R,…

Q: Let A = follows: For V(a,b), (c,d) = A x A, (a,b)R(c,d) ⇒ a ≤ c and b ≤ d {0,1,2} and the partial…

A: a. The Hasse diagram is shown below.

Q: The relation R defined on a set A is antisymmetric if (a, b) ER = (b, a) E R for (A) Every (a, b) ER…

A: A relation R is said to be antisymmetric if (a,b)∈R and (b,a)∈R implies a=b

Q: A relation < is defined on R? by (x1, x2) < (y1, y2) if and only if x1 < yi and x1 + x2 2 yı + y2.…

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. Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let P = P(A) be the power set of A. Let R be the relation on…

A: (a) For any X ∈ P,            | X ∪ X | = |X|           | X ∪ {1, 2} | = |X| + |{1, 2}| - |X ∩ {1,…

Q: on P(X), where X = Y, Z E P(X), we say Y - Z if and only if Y has the same number of ele- Define a…

A: Given a set X={1,2,3,4,5,6}. Define a relation ~ on P(X) as : For Y,Z∈ P(X), we say  Y~Z if and only…

Q: 2 Relations For the following relation R over the integers, prove whether R is or is not: 1.…

A:

Q: 8. Define a relation on Z as xRy if |x-y| < 1. Is R reflexive? Symmetric? Transitive? If a property…

A: Given, Define a relation on Z as xR y if |x-y| &lt; 1. we have to find Is R reflexive? Symmetric?…

Q: Let A = {6, 8, 13, 15, 9, 16} and define a relation R on A as follows: xRy ⟺ 7 |(x – y) Draw a…

A:

Q: On sets, the relation x R y given by there exists a bijective function from the set x to the set y'…

A:

Q: 4) The relationk onthe Selof real numbers Risa partialorder relation.

A: relation R on a set A is called a partial order relation if it satisfies the following three…

Q: (b) Observe that all the relations in (a) are equivalence relations. Prove that this is true in…

A: Given: A is a nonempty set, and P is a partition of A. To show: The relation R is equivalence…

Q: (4) Let T be the partial order relation on P({1,2,..., 20}) defined by ATB if and only if |A < |B|…

A: Question: Let T be the partial order relation on P1,2,...,20 defined by ATB if and only if A&lt;B or…

Q: Let A = {1,2, 3, 6}. Define a relation R on A as follows: x Ry if y – x > 0 Write out the relation R…

A: We have to find the relation and write as set notation.

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: R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows:…

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: Given set A = {1, 2, 3, 4}, mention 5 or more relations (R) defined on A such that R does not…

A:

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: Let A = {1,2,3}, X = {1,3}, and R is a relation on A, such that R= {(x,y) | x<y ^ x, y = A} R"X =…

A: , and is a relation on .

Q: Prove. For any x, y ∈ R and x < y, ⟨(x, y), ≤⟩ is not well-ordered, where (x, y) is an open interval…

A: To Prove: x,y,≤ is not well ordered, where x,y is an open set with the usual order "≤".

Q: Consider relation R={(x,y)|x divides y,xEA,y€A} on the set A={2,3,4,5,10,12,25,30}. (a) Check…

A: We are given a relation : R={(x,y)|x divides y,x∈A,y∈A}  on a set A={2,3,4,5,10,12,25,30}

Q: R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows: (X:V1)< (x2,…

A: The relation ≺ is defined as follows:  x1,y1≺x2,y2 if and only if x1&lt;x2 or x1=x2 and y1≤y2

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

A: Answer :

Q: 5. Let X be the set X = {1,2,3}, and let R be the relation defined on X by x₁ Rx₂ if x1 + x2 3. (a)…

A:

Q: 18. Let X be a set. Define a relation R on P(X) by ARB AN B = ) for A, BE P(X). Determine whether…

A: We will use the definition of reflexivity, symmetry and transitivity to check the following :

Q: 6.3. Let (A, <A) and (B,<B) be two partially ordered sets. One can define on the cartesian product A…

A: Given: A, ⩽A and B, ⩽B are partially ordered sets.  A Cartesian product A x B is defined with…

Q: 3.7 Consider a fuzzy relation R CAXA where A = {a, b, c}. R a b e 1 1 1 1 1 1 d 1 1 1 a) Determine…

A: Solution :-

Q: 4. Let (X,≤) be a partial ordered set. Show that a subset A of X has at most one least upper bound.

A: Given that   be a partial ordered set and A is a sub set of X.Now we want to prove that A has at…

Q: (Relations) Consider the set A = {1,2, 3, 4, 5}, and a relation R defined by x Ry + x² – y is an…

A: Since you have posted a multipart question and we can answer three subparts. So, answered the first…

Q: Consider the subset R = R × R − {(x, x)|x ∈ R}. What familiar relation on R is this? Explain.

A: Concept used: Subset relation Subset relations are used to define partial orderings on sets. A set's…