11. Let X be a set and be an equivalence relation on X. Prove that for x,y e X, if xy, then [x][y] = 0.

Q: - Recall that for x, y € R, x - y = R is the absolute value of x-y. That is, if x-y 20 if x-y<0. x-y…

A:

Q: 1. Let A = Z+x Z. Let R be a relation defined on A as follows: For all (a, b), (c, d) € A, (a, b) R…

A:

Q: Recall that a |b is a relation on the natural numbers meaning “a divides b.” It is defined by a |b…

A:

Q: Answer the following question accordingly:

A: Given set is  B={1,2,3,4}

Q: Show that “is unitarily equivalent to” is an equivalence relation on Mn×n(C).

A:

Q: 4. (a) Let R be the set of all real numbers. Consider a relation S on R, i.e. SCRX R. which is…

A: Thank you

Q: 5. Let R be an equivalence relation on a set A. Prove that for all a, b E A, a R biff [a] = [b].

A:

Q: 4. Let R be a relation on the set of all integers. xRy iff x - y = 3m for some integer m. Show that…

A:

Q: Let R be a relation on the set A = {x € Z:1 < x < 100} defined as follows: x R y if and only if x-y…

A: Equivalence relation

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: Let I be the set of all straight lines in the plane. Define and equivalence relation R by x R y iff…

A: Let, R be a relation on L(set of all straight lines in the plane) defined as, xRy iff x and y are…

Q: Define the relation R on Z as follows: for x, y ∈ Z, xRy if and only y−x ≥ 0. Determine whether R is…

A: partial order means reflexive and antisymmetric.

Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: Q7. Let R be a relation on the set Z defined by the following rule: for all a, b e Z, a Rb if and…

A:

Q: 9.29. Let R be an equivalence relation defined on a set A containing the elements a, b, c and d.…

A:

Q: 1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the…

A: The given problem is to prove that the relation is equivalence relation, to be equivalence it must…

Q: Let C be a relation defined on the set of all geometric polygons, defined by any two polygons in the…

A: The given problem is from relation on sets. Here. Give that C be a relation defined on the set of…

Q: In each of the following cases of a set X and relation determine whether ~ is reflexive, symmetric,…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 11. Let A be a nonempty set and let ~ be an equivalence relation on A. Prove each of the following:…

A:

Q: You are the owner of a gourmet diner. On Wednesday nights, you offer a special of "Buy one dinner,…

A:

Q: 6. Let (a, b), (c,d) E R2. Define a relation ~on R2 by [ (a, b)~ (c,d) if |ab|=|cd| Show that is an…

A:

Q: (1) Show v is an equivalence relation on S. (2) Describe the equivalence classes of . (3) Describe…

A: Given: Define ~ on S=a, b: a, b∈ℤ, b≠0 by a, b~c, d if and only if ad-bc=0. To show: 1) ~ is an…

Q: 5. Let A = {6, 8, 10, 15, 17} and B = {2, 3, 4, 5} and define a relation R: A → B as follows: For…

A: Given: A={6, 8, 10, 15, 17} B={2, 3, 4, 5} Relation R:A→B is: For all x,y∈A×B∈R if and only if…

Q: 3. For universe S = R² define relation ~ as: (a, b) ~ (c,d) ⇒ 2a-b2c - d. Prove that is an…

A:

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: Lex 172,3,4). Consider the relation R on X defined as follows. R = ((1.1), 13), (2,2), (2.4), (3,1),…

A: I have solved both subpart using basic definition of equivalence relation and equivalence class.

Q: 17. Prove that if R is a symmetric, transitive relation on A and the domain of R is A, then R is…

A:

Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…

A:

Q: A relation on a set A is circular iff , y, z x~y and y~z implies z~x. Prove that a relation is an…

A: The relation on a set is a subset of the Cartesian product of the set. Therefore, each element is in…