defined are the relations ≡6 and ≡10 to be certain subsets of Z^2 . Their intersection R = (≡6)∩(≡10) is another subset of Z^2 , so it is also a relation on Z. b) The relation R is equal to ≡m for some natural number m. Then i found out that m is 30... so the question is " Based on your answer to part (b), complete the following statement with a formula for p in terms of m and n, and write down a proof of your statement. Let m and n be positive integers. Then (≡m) ∩ (≡n) = (≡p), where p = .......

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: In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric,…

A: Since you have asked  multiple questions so as per guidelines we will solve  the first question for…

Q: Let a,b,c,d be real number with a < b < c < d. Express the set [a,b] U [c,d] as the difference of…

A: We have given that, a, b, c, d are real numbers with a &lt; b &lt; c &lt; d. We need to express a, b…

Q: The relation D is defined on the set P = {6, 9, 15, 54, 78, 90} by the rule: n1 D n2 exactly if (n2…

A: (i) The relation D is defined on the set P=6, 9, 15, 54, 78, 90 by the following rule: n1 D n2…

Q: NXN set on " (a,b)~ (c,d) -) a+d -b+c %3D define d as, equiualence relation? Shaw Is reation ""

A:

Q: We have defined the relations ≡6 and ≡10 to be certain subsets of Z^2 . Their intersection R =…

A:

Q: A relation ~ is defined on the set of all pairs of integers by the formula (m,n) ~ (u,v) m - An =…

A:

Q: If #: $ a,b,c} which of these celations are a funchion? Emplain, cab) CS

A: Solution : Given :    A= {a, b, c}  Set of relations are      a)    { (a, b), (b, c), (c, c) }…

Q: artial order relation but not a e, cTd, aTe and eTd. ersi diagram for each possible rela

A:

Q: 9. The relation ~ defined on the set of natural numbers by a ~ b means 'a – b is even is : A. an…

A: Equivalence relation : A relation which is reflexive, symmetric and transitive is an equivalence…

Q: 1. Verify that the relation ~ is an equivalence relation on the set S given. (a) S = R reals, a ~ b…

A:

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: Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a = b…

A: The objective of the question is to determine which of the given relations are symmetric and…

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: For each relation, indicate whether the relation is: \ item Reflexive, anti-reflexive, or neither \…

A: (a) From the given data the relation is xLy if x&lt;y. (i)For every x∈ℝ,  since x is not less than x…

Q: Consider the following sets V = W = X = Y = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} {p EN:p is a prime…

A:

Q: A relation R is defined on the set of natural numbers N={1,2,3...}  as follows: aRb means "b=a+6/a;…

A: Domain means all the values that can be taken so that the aRb is defined.

Q: Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a =…

A:

Q: 8) Let a 3-2 +45 for n-0, 1, 2, 3,... If we write an as a recursive relation, it is Hint: calculate…

A: 8) Given an=3.2n+4.5n for n=0,1,2,3,...   To Find: an as recursive relation

Q: Let R be the set of real numbers, C= (0, 10], D= (9, 15], E = {1, 2, 3} and F= (7, 10). Find: (i)…

A:

Q: 2.) Suppose A is a set with 4 elements and B is a set with 3 elements. How many relations are there…

A:

Q: Please answer the part (B). I have got a solution for the question on this platform but the answer…

A:

Q: There are 3 parts to this question. The answer choices for each are all. 1) reflexive 2) irreflexive…

A:

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

A:

Q: 6. Consider the set R2 and relation~: (1, 1)~ (2, 2) if and only if x2 = ₁ + m and y2 = ₁ +n for…

A: We shall solve only the first and second part of the question. If you want to solve the remaining…

Q: 1(b). Is (p->q)->[(p->q)->q] a tautology? Why or why not?  (c). Given the relation on the set .…

A: We are entitled to solve only one question at a time. Please submit another question separately. To…