week2 Relations

 0    11 schede    up804653
Scarica mp3 Stampa Gioca Testa il tuo livello
 
Domanda English Risposta English
Define Cartesian product
inizia ad imparare
a Cartesian product is a mathematical operation that returns a set from multiple sets
What is the Cartesian product of two sets: A = {a, b} and B = {5, 6}.
inizia ad imparare
defining two sets: A = {a, b} and B = {5, 6}. Both set A and set B consist of two elements each. Their Cartesian product, written as A × B, results in a new set which has the following elements: A × B = {(a,5), (a,6), (b,5), (b,6)}.
Define from to relations
inizia ad imparare
LetAandBbe nonempty sets. A (binary) relationTfromAtoBisa subset ofA B. IfT A Band(a,b)2T, we say thatais related tobbyT, aTb
What is the more common way of describing relations?
inizia ad imparare
\by characteristics of their elements"
give an example of a relationship defined by charicteristics
inizia ad imparare
x ∈ A is related to y ∈ B if and only if x<=y
What is a relation on a set
inizia ad imparare
When A=B then a (binary) relation on A is a relation from A to A, hence a subset of A * A
Explain the property reflexiveity
inizia ad imparare
R is reflexive if and only if(x,x) ∈ R for all x∈ A.
Explain the property symmetry
inizia ad imparare
R is symmetric if and only if for all x, y ∈A if (x,y) ∈ R then(y,x)∈R
Explain the property transitivity
inizia ad imparare
Ris transitive if and only if for all x, y, z ∈ A if(x,y) ∈ R and(y,z) ∈ R then(x,z) ∈ R
Explain the property equivalence
inizia ad imparare
Ris an equivalence relation if and only ifRis re exive, symmetric, and transitive
Explain Equivalence class
inizia ad imparare
Suppose A is a set and R is an equivalence relation on A. For each elementain A, the equivalence class of a,[a], is the set of allelementxinAsuch thatxis related toabyR:[a] =fxjx2Aand(x,a)2Rg

Vedi schede correlate:

Week 3 FunctionsWeek 4 Logic

Devi essere accedere per pubblicare un commento.