Search results with tag "Equivalence relation"
![[Ch 8] Relations 1. Basics - DePaul University](/cache/no-preview.jpg)
[Ch 8] Relations 1. Basics - DePaul University
condor.depaul.eduEquivalence Relations • A relation on a set that satisfies the three properties of reflexivity, symmetry, and transitivity is called an equivalence ... R is symmetric because whenever (x,y) is in R, (y,x) is in R as well. R is transitive because whenever (x,y) and (y,z) are in R, (x,z) is in R as well. Consider the relation R on a set {1,2,3 ...
EECS 203-1 Homework 9 Solutions Total Points: 50
www.eecs.umich.eduwe know that ad = bc, and cf = de, multiplying these two equations we get adcf = bcde => af = be => ((a, b), (e, f)) ∈ R Hence it is transitive. Thus R is an equivalence relation. 14) Determine whether the relations represented by the following zero-one matrices are equivalence relations. 4 points a) 1 1 1 0 1 1 1 1 1
Equivalence Relations - Mathematical and Statistical Sciences
www-math.ucdenver.eduModular Arithmetic Theorem: For any natural number m, the modular relation ≡ m is an equivalence relation on ℤ. Pf: For any x in ℤ, since x – x = 0 and m | 0, x ≡ m x. (Reflexitivity) If x ≡ m y then m | x – y. Since y – x = -(x-y), m | y – x, and so, y ≡ m x. (Symmetry) If x ≡ m y and y ≡ m z then m | x – y and m | y ...