
#1
May310, 07:06 AM

P: 14

1. The problem statement, all variables and given/known data
Find the equivalence class [2] for the following equivalence relations: a) R: Z <> Z, where xRy, iff x = y b) T: N <> N, where xTy, iff xmod4 = ymod4 N means natural numbers etc...there wasnt the correct symbols in the latex reference 2. Relevant equations ?? 3. The attempt at a solution Ok so I know how to do the b) part, because we had examples at the class, its: [0] = {0,4,8,12,...} [1] = {1,5,9,13,...} [2] = {2,6,10,14,...} so the answer is [2] = {2,6,10,14,...} right? but i dont know how i start to build it when i have x = y its probably something very easy and i just dont get it for some reason 



#2
May310, 07:11 AM

Mentor
P: 6,040

Suppose x is given but unknown, and that x = y. What can y equal in terms of the given x?




#3
May310, 07:33 AM

P: 14

hmmm...y must always be +x or x?
but i dont understand how the classes are formed. For example class [0], does it mean the list starts at 0? In the bpart the list increases always by 4, but what about in this, by 1? 



#4
May310, 07:38 AM

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P: 6,040

Finding Equivalence Class
Now think about concrete examples. If x = 3, what can y be? Consequently, what is [3]?




#5
May310, 07:50 AM

P: 14

if x = 3, then y can then be 3 or 3
What is [3]? I dont know, {..., ???, 3, ???, ...} 



#6
May310, 07:59 AM

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P: 6,040

Do you understand why the answer to b) is the answer to b)? Back to a).
[x] = {y  xRy} = {y in Z  y = x} [3] = {y  (3)Ry} = {y in Z  y = 3} 



#7
May310, 08:27 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,886





#8
May310, 08:39 AM

P: 14

I thought I understood the b) part, but now im not sure if i do deeply enough.
So, in each class the elements are "equivalent" in the way the equivalence relation is defined? xmod4 = ymod4 means every element which has same modulus when divided by 4 belong to same class? can [3] then be only {3,3} in the a) part? And [2] = {2,2} etc? I'm confused because we only had those modulus examples in the class and in book and I dont think I understood the theory deeply enough =) 



#9
May310, 09:01 AM

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P: 6,040

What about [0] in a)? 



#10
May310, 09:12 AM

P: 14

[0] must then be only {0}
What about R: R <> R, where xRy, iff floor(x) = floor(y) i dont know if floor() is the right way to write floor function, but cant find the correct symbol. [2] is then something like {2, 2.1, 2.2, ... , 2.99999...} but what is the correct way to write it? Because 2 can have any amount of decimals after it. Does it have to be in a list form like a) and b) here was? Thanks much for the replies, you helped me alot! 



#11
May310, 09:20 AM

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P: 6,040





#12
May710, 01:21 PM

P: 59




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