Income Question
Given that
A= {0,1,2,3,4}
R = {(0,0),(0,4),(1,1),(1,3),(2,2),(3,1),(3,3),(4,0),(4,4)}
Answer:
See Explanation Below
Step-by-step explanation:
a.
The equivalence class of A, is the set of all elements x in A such that x is related to A by R
Let ~ be a equivalence relation on set A such that x ∈ A and y ∈ A such that x ~ y.
Meaning that x is an element of A and y is an element of A where x = y
Considering the given data.
A= {0,1,2,3,4}
R = {(0,0),(0,4),(1,1),(1,3),(2,2),(3,1),(3,3),(4,0),(4,4)}.
We find that;
(0,4) ∈ R; so 0 and 4 belong to a class
(1,3) ∈ R; so 1 and 3 belong to a class
(2,2) ∈ R; 2 doesn't occur in any other pair in R; So, 2 is in its own class.
To prove that R is an equivalence relation;.
We set A/R
A/R gives {(0,4),(1,3),(2,2)}.
So, R is an equivalence of A.
b. All possible equivalence classes in R = {(0,4),(1,3),(2,2)}
