n R m in Z if nm>0

Q: You just bought a new car from a dealership that sells cars no older than 2015. Consider the…

A: According to the given information, Let S be the set of all cars sold in the period 2015 to 2020.…

Q: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

A: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

Q: 5. Let S be the set of all the nonempty subsets of 2={a,b,c,d}. Define a relation R on S as follows:…

A: Any Relation is said to be equivalent if  it Reflexive , Symmetric and Transitive

Q: (b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs…

A:

Q: Let A = (a, b, c) and R = ((a, a), (b, b), (c, c), (c, b), (b, c)). Which of the following statement…

A: Given set is  A = {a, b, c} and  R = {(a,a), (b,b), (c,c), (c,b), (b,c)} is relation on A

Q: 2. Let A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and suppose R is a relation defined by a is related to b…

A: Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

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: Q 7 Let S andT be equivalence relations on a set B. (a) Prove that the intersection SnT is an…

A: a) Given:        An equivalence relation is a binary relation that is reflexive, symmetric, and…

Q: Let A = {2, 3, 4, 6, 7, 9} and define a relation R on A as follows: For all x, y e A , x R y = 3…

A: Given A = {2,3,4,6,7,9} xRy ⇔ 3 divides (x-y) Therefore 1)  R = (2,2) , (3,3) , (4,4) , (6,6) ,…

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: Let A = {-6, -5, -4, -3, -2, -1, 0, 1, 2} and define a relation R on A as follows: For all m, n E A,…

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: Recall that, for any set A, the power set of A, P ( A ), is the set of all subsets of A. Consider…

A: To  find if the inclusion relation on P(A) has the properties of reflexivity, symmetry and…

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

A: a equivalence class is a subset of the set on which the relation R is defined such that all elements…

Q: Consider the following relation R on the set Give an example of a pair that is not in R, but in the…

A:

Q: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

A: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

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

A:

Q: Check if the following statement is TRUE or FALSE. Let R be an equivalence relation on a nonempty…

A:

Q: Let A = {-3, -2, -1, 0, 1, 2, 3, 4, 5} and define a relation R on A as follows: For all m, n E A, m…

A: The given set A is -3,-2,-1,0,1,2,3,4,5 and relation is defined on A is  For all m,n∈A, m R…

Q: Given set A = {1, 2, 3} and S = P(A) The relation is defined as xRy ⇔ |x| = |y| Indicate the…

A:

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: Which ONE of the following represents an equivalence relation on the set of integers? Vx.y€Z, xRy if…

A:

Q: Prove and say the name of the following equivalence relation x ~ y ⟺ x - y = 4k, k ∈ Z

A: x ~ y iff x - y = 4k , k in Z Implies that  x is congurent to y mod 4.

Q: Let R be the relation, {(a, b) e N x N:a + b is odd}. Give an example that shows that R is not…

A: Given R be the relation, {(a, b) ∈ N x N:a + b is odd}.  We find an example that shows that R is not…

Q: A relation is an equivalence relation if it satisfies three properties. which of the following…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Define a binary relation on the set S=(-3, -2, -1, 1, 2, 3} as follows: R= {(a,b) ab>0} %3D a. Find…

A:

Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b}.…

A:

Q: The 2-tuples (ordered pairs) of integers is the set Z x Z and can be given an equivalence relation…

A: The given set is ℤ×ℤ, where ℤ is the set of all integers. So basically ℤ×ℤ is the set of all ordered…

Q: 3. Let R be a relation defined on Q by: Ga) ER if ad = bc a) Show that R is an equivalence relation…

A:

Q: Determine whether the given relation is an equivalence relation on the set: n R m in Z if nm>0.

A: Given a relation : n R m in ℤ if nm&gt;0 i.e. n is related to m in the set of integers if nm is…

Q: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

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 or not the following relations are equivalence relations on the given set. If the…

A: Let m, n, p∈ℚ Relation is m~n in ℚ if mn≥0 (i) Reflexive: Let m∈ℚ then mm=m2≥0 Therefore m~m   ∀m∈ℚ…

Q: Let the relation R on the set Z be given by the condition: (x, y) E Rif and only if x4 = y4. Answer…

A:

Q: Determine if the relation described is an equivalence relation on the given set. Let S = Z+, a ~ b…

A:

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

A:

Q: Let - be a relation on a set X defined as below. Determine whether is an equivalence relation on X…

A:

Q: Let A # 0 be a set. Prove that A? is an equivalence relation on A.

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: You just bought a new car from a dealership that sells cars no older than 2015. Consider the…

A:

Q: 6. Prove the following statements and provide an illustration to substantiate the proof. a) Let R1…

A: (i), (ii) &amp; (iii) implies R1 intersection R2 is an equivalence relation.

Q: Determine whether or not the following relations are equivalence relations on the given set. If the…

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: Determine whether or not the relation ? on the set of all people is reflexive,  symmetric,…

A:

Q: Let R be the following relation on the set of all people. R= {(a, b) : a and b share a common…

A:

Q: Let X = {−1, 0, 1} and A = ?(x) and define a relation R on A as follows: For all sets s and t in…

A: Given the set X=-1,0,1. Consider the set A as the power set of X given by A=PX. Since the set X has…

Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

A:

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

A:

Q: Prove that the given relation is an equivalence relation, and describe the distinct equivalence…

A: Let A is the set of all students at your college. For every x,y∈A,  xSy⇔x is the same age as y. That…