tiv Consider the relation defined on Z by m~n if and only if m+n is eve (a) Show that ~ is an equivalence relation. How many equivalence class does ~ have? explain. (b) Repeat (a) with , where m~n if and only if m+2n is a multiple

Q: what are the steps you take to find the equivalence classes? I still don't really understand why…

A: To determine the distinct equivalence classes of the relation R defined on Z (the set of integers)…

Q: Let A = {1,2,3,4} and B = {5, 6, 7}. Let f be the relation f = {(1,5). (2,5), (3,6), (?, ?)} where…

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: Give a specific reason why the following set R does not define an equivalence relation on the set…

A:

Q: How many equivalence relations on the set {1, 2, 3}?

A: Given A=1,2,3 we know that a relation is said to be equivalence relation if it is reflexive,…

Q: Let~ be the equivalence relation on Z defined by a ~ y if and only if x - y is divisible by 5. How…

A:

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

A:

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: The congruence modulo 5 relation is an equivalence relation on the set {0, 1, 2, 3, 4, 5, 6, 7,8,9,…

A:

Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

A: We will find out the required value.

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 the relation - on the natural numbers N be defined as follows: if n is even, then n ~ n + 1; if…

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: What are the equivalence classes of the equivalence relations on {0, 1, 2, 3}?

A: Answer:-  Find the equivalence classes of the equivalence relations on A = {0, 1, 2, 3}?

Q: Let R be the relation defined on Z by aRb if a + b is even. I have the following equivalence classes…

A:

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

A:

Q: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b)} : a is…

A:

Q: Which of the following is an equevalence relation on the set (a, b, c} 7 O (a, a), (a, b), (b, a).…

A: Option 1 is equivalence relation. Option 2 is also is an equivalence relation. Option 3 and 4 is not…

Q: Let X = {1, 2, 3, 4, 5, 6}. Which of the following could be an equivalence class of an equivalence…

A: Equivalence class on a set

Q: 13. Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of…

A: The relations on 0, 1, 2, 3 are given as: (a) 0, 0, 0, 2, 2, 0, 2, 2, 2, 3, 3, 2, 3, 3 (b) 0, 0, 0,…

Q: 6. (a, b), C

A: Let R be the relation on the set of ordered pairs of positive integers such that a,b,c,d∈R if and…

Q: 7. Let A = {1,2,3,4}x{1,2,3,4}. Define an equivalence relation ~ by (x1,x2) ~ (x3,xa) iff xxx2 =…

A: Let A=1,2,3,4×1,2,3,4. The equivalence relation ~  is defined by,        "x1,x2~x3,x4 only if…