CP 4 Relations 2

Question 1

• STATEMENT
  Let δ be a set whose elements are “a set of sets” noted Up∈sP (a union of all sets in S

Answer 1

if S={{1,2,5},{2},{2,7,8}{3}}
then Up∈sP =
{1,2,5,7,8,3}

Question 2

We say δ partitions X if

Answer 2

Up∈sP=X
- union of all elements in δ is = X

Question 3

TF a partition of X can contain an element thats not included in X

Answer 3

F, all partitions of X must strictly contain all the elements of X

Question 4

TF we can have duplicate elements in a partition

Answer 4

F we cannot becuase we need the ∩ of all sets in the partition to = {}

Question 5

what is an equivalence class

Answer 5

given a∈X the equiv.class is
[a] = {b∈X|(a,b)∈R}
- In simple terms: an equivalence class is like sorting things into buckets where everything in a bucket is “the same” according to a specific rule!

Question 6

what is the set of equivalence classes

Answer 6

defined to be S/R={[a]|a∈X}
- so find the eq class of every element in set X and make them a new set

Question 7

what the criteria for an equivalence classq

Answer 7

Must be reflexive, symmetric and transitive

Question 8

What is the denotation S/R

Answer 8

The set of equivalence classes