For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show which qualities of an equivalence relation it lacks: {(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)} { (0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 2), (3, 3)}

Q: Let x1, x2, y1, y2 be real numbers. The expression (x1, y1) ~ (x2, y2) means that x12 + y12 = x22 +…

A:

Q: List the ordered pairs in the equivalence relations produced by these partitions of (0, 1, 2, 3, 4,…

A: Solution: If P=A0,A1,.....,Ak be a partition of a set A then the partition generates an equivalence…

Q: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

A: we have given a set  A = { 1, 2, 3, 4}  and R is a relation on the set A where R is defined as (a,…

Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

A:

Q: The real line R is divided into subsets X1, X2, X3 where X1 = (-00, – 7], X2 = [-7,1), and X3 = [1,…

A: Infinite sets can also be grouped into equivalence classes, such that all the sets in a given…

Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show  which…

A:

Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

A: By definition of  relation it is define as A relation is symmetric if and only if (b, a) ∈ R…

Q: Please choose the correct answer. Thank you If X={1, 4, 7} and Y={2, 3} and define a relation R…

A: The connection between two sets is defined by a relation. If set A has relation with set B , then…

Q: Let R CR* x R† with R = {(x, y)|[x] terms of whether it is reflexive, irreflexive, symmetric,…

A: Consider the given information:

Q: Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5, x is a natural…

A:

Q: ' (a,b) ∼ (c,d) ⇔ a+d =b+c '' defined as '∼' relation is that a equivalence relation?

A: It is equivalence relation if (a, b) belongs to ZxZ

Q: If R is reflexive, symmetric and transitive then the relation is said to be--------

A: Any relation R on a set S is equivalent if and only if it follows the below conditions: (a) R is…

Q: The domain for the relation R is Z × Z. (a,b) R (c,d) if and only if a <c and b< d. Indicate whether…

A:

Q: Enter an example of an equivalence relation R on the set X = {0, 1, 2, 4, 8) such that all of the…

A: We need to find an example of an equivalence relation on set X=0,1,2,4,8 such that: 1,4∈R 8,4∉R…

Q: 5. Let a and b be real numbers, not both zero. For (71, y1) and (12, 42) in R², set (11, yı) ~ (12,…

A:

Q: Let R be the relation {(1,2),(1,3),(2,3),(2,4),(3,1)}, and let S be the relation…

A:

Q: Let B= {0,1,2,3,4} and let 0} , 1,3,4|,|2} be a partition of B that induces a relation Q. Find the…

A: Consider the given information.

Q: properties:Reflexive,Symmetric and Transitive. a R b iff a+b is evenly divisible by 3 b)Does this…

A:

Q: Let A = Z and B = Z\{0}. Show that the relation R on A x B defined by (a, b)R(c, d) if ad = bc, is…

A:

Q: Check whether Ris reflexive, symmetric or transitive and hence determine whether the relation Ris…

A:

Q: а. {(0,0), (1,1), (2,2), (3,3)} b. {(0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3)} с. {(0,0),…

A:

Q: binary relation R is defined on the set of real numbers by xRy ⇔ lx - yl ≤ 1. Determine whether or…

A: R is not an equivalence relation. Because, R is not transitive. The Counter example is as follows…

Q: 22) (a) Show that the relation {(0,0), (1,1),(1,2), (2,1), (2,2), (3,3)} is an equivalence relation…

A: Given 0,0,1,1,1,2,2,1,2,2,3,2

Q: Q2. (a) Find the equivalence class [-3]5 (b) Find the ordered pairs of the relation R from the set A…

A: We have to answer the following questions :  (a) Find the equivalence class  -35 (b) Find the…

Q: The domain of relation R is ZxZ. (a, b) is related to (c, d) if a s c and b s d. Which statement…

A: In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and…

Q: Determine whether the given relation is an equivalent relation on {1,2,3, 4, 5}. If the relation is…

A: Equivalence class of an element a is given by [a] such that [a]={b:(a, b) lies in R}

Q: Q5) Let X = {a, b,c, d} and let R = { (a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (b, d), (d,…

A: Given : X = a, b, c, d R = a, a, a, b, a, c, b, a, b, b, b, c, b, d, d, d be a relation.   To show…

Q: Let R be the relation on A × A, where A = {1,2,3,4}, that is, ele- ments of this relation are pairs…

A:

Q: Determine whether the relation is reflexive, symmetric, antisymmetric and transitive. Provide one…

A:

Q: Let R ⊆ ℝ×ℝ with R={(x,y)|⌈x⌉=⌈y⌉}, that is, x and y round up to the same number. Characterize R in…

A: Given problem is :

Q: x R y in R if x- y < 3 |

A: Note that for any real number x, |x-x|=0&lt;3.  Thus, xRx or the given relation is reflexive.

Q: Determine whether the following relations are equivalence relations. For those relations that are…

A:

Q: Check whether the following relations are reflexive, symmetric, transitive and anti-symmetric and…

A:

Q: Describe the equivalence classes of the relation R = {(a, b) : a E Z,beZ, 13 divides (a - b)}

A:

Q: Essentials of DISCRETE MATHEMATICS   Q: Shot that the relation “congruency modulo n” is an…

A: We have to show that the relation “congruency modulo n” is an equivalence relation.

Q: Let R be the relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by the rule (a,b) eR if the…

A: Given: A={1, 2, 3, 4, 5, 6, 7} and R is the relation on this set defined s: (a, b)ϵR of the integer…

Q: Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as follows:…

A: We have to Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as…

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that R ∪ S is…

A:

Q: Check the following relation R on the set A = {1, 2, 3, 4]} is reflexive, symmetric and or…

A:

Q: Which of these relations on {0,1,2,3} are equivalence relations or a partial order? Determine the…

A:

Q: b. Let us consider the sets A = {2,3,4,5} and B = { 0,1,2,3}. Define the relation R: A → B such that…

A:

Q: Show that the relation R is an equivalence relation in the set A = { 1, 2, 3, 4, 5 } given by the…

A: Given- Set A={1,2,3,,4,5}. To Show- That the relation R is an equivalence relation in the set A = {…

Q: a) If R and S be two relations from set A to B. Show that (RNS)-¹ = R-¹ S-¹ b) Justify the following…

A: We know that ,  A relation R defined on a set A is called equivalence relation if R satisfies the…

Q: Let R C R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given, R⊆ℝ+×ℝ+ with               R= x, y | x=y

Q: . Let R be a relation defined on the set A = N x N where (a, b) R (c, d) if a³ s an equivalence…

A: Introduction: Any two elements are said to be equivalent if they have an equivalence relationship. '…

Q: Decide whether the following relations is an equivalence relation or not. {(x, y) | xy > 0, x and y…

A:

Q: A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain…

A:

Q: Explain why consimilarity is an equivalence relation on M,.

A: Given that consimilarity is an equivalence relation on Mn.

Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show which…

A: Either show the following relations on {0, 1, 2, 3} is an equivalence relation,

Q: Determine whether the given relation is an equivalent relation on {1, 2, 3, 4, 5}. If the relation…

A: