7. Let P be the congruence modulo 6 relation. Note, this is an equivalence relation. a. List 5 numbers x such that 1Px. How do you know these numbers are related to 1?

Q: 3. Let the relation R on X = {1,3,5, 6, 8, 9, 11} be such that xRy means "x – y is a multiple of 3".…

A:

Q: 3. The DIIOwing relations are not equi properties that are not satisfied. Explain your answer. a. a…

A:

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

A: 11. Let A be a nonempty set and ~be an equivalence relation on A. (b)  We know that for each a, b∈A…

Q: The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation. I know the…

A: The objective of the question is to understand how to find the numbers that satisfy the given…

Q: Proposition 2.12. Suppose- that R is an equivalence relation on a set A, and let a, b e A. Then the…

A: Given below the detailed Solution

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: y = - 1.5 cos (3x -90) +0.5   what is the    a) period  b) amplitude  c) the phase shift

A: Since you have uploaded multiple part questions according to our guidelines we have solved the first…

Q: 1. In the diagram below, there are 9 points and 8 lines: (a) Let be the relation between the points…

A: Given, In the diagram below, there are 9 points and 8 lines. a) Let ⋄ be the relation between the…

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: For set S = {1, 2, 3, 4}, we define the following relations R1 = {(2,2), (2, 3), (2, 4), (3, 2), (3,…

A:

Q: R is a relation on the set of positive integers such that xRy iff log base 2 (x/y) is an integer. Is…

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: Let R be a relation defined on the set of integers as follows: a R b iff 6 divides  (a - b). R is…

A:

Q: Determine whether each relation is an equivalence relation. Justify your answer. If the relation is…

A: According to the given information it is required to check whether the given relation in each part…

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: Exercise 17.2.18. Find binary relations on {1,2,3} that meet each of the following conditions.…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

Q: The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation. the equivalence…

A: The objective of the question is to understand how the equivalence classes for the given equivalence…

Q: Discrete Math: Lets say B = {1,2,3,4,5,6}. Let R be the smallest equivalence relation on B which…

A:

Q: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

Q: Let A = {a, b, c, d, e}. Suppose R is an equivalence relation on A. Suppose R has two equivalence…

A:

Q: Consider the binary relation for "less than" with the symbol <. This relation does not define an…

A: Reflexive relation: A  relation S on a set A is called reflexive relation if every element of set A…