Thread: help me find the ordered pairs for (x,y)∈r if 3 divides x-y (relations)

i need to figure out relations, and to that we were taught to find ordered pairs and then put them in a matrix, and then i can determine if this equation is reflexive, stymeteric,antisymmertic and so.

i don;t know how to figure out what the ordered pairs are though.

Originally Posted by madmilitia

i need to figure out relations, and to that we were taught to find ordered pairs and then put them in a matrix, and then i can determine if this equation is reflexive, symmetric, asymmetric and so.

First, you must know on what set the relation is defined. You failed to do that.

Second, I have no idea what put them in a matrix could mean. So please tell us.

Third, do you know what reflexive, symmetric, asymmetric mean?

Now I will give you three pairs in the relation on

Originally Posted by madmilitia

i don;t know how to figure out what the ordered pairs are though.

You could start by reading the introduction of the Wikipedia article about ordered pairs and then writing, say, 6 ordered pairs (x, y) of integers such that 3 divides x - y. Note that it is my guess that elements of pairs are integers. The problem that you are trying to solve is supposed to specify the set on which the relation is considered.

Originally Posted by madmilitia

i need to figure out relations, and to that we were taught to find ordered pairs and then put them in a matrix

You can write the matrix corresponding to a relation if the relation is on a finite set. If this relation is indeed considered on the set of all integers, then the matrix would be infinite.

Originally Posted by Plato

First, you must know on what set the relation is defined. You failed to do that.

Second, I have no idea what put them in a matrix could mean. So please tell us.

Third, do you know what reflexive, symmetric, asymmetric mean?

Now I will give you three pairs in the relation on

sorry about that, yes i know what reflexive, symmetric, asymmetric mean

the question is "determine whether each relation defined on the set of positive intergers is reflexivem symmetric,antisymmertic,transitive, and or partial order.

then it gives 5 problems but the first and the one i'm trying to figure out is. x,y)∈r if 3 divides x-y



(x,y)∈r if 3 divides x-y to do this we need to figure out the elements of R so we can get our ordered pair. Those elements are (1,1),(1,2)(1,3)(2,1)(2,2)(2,3)(3,1)(3,2)(3,3)(4,4 ) with this ordered pair we can fill in our matrix. From the matrix we can see that this is an equivalence relation.
x x x x x
y 1 2 3 4
Y 1 x x x o
Y 2 x x x o
Y 3 x x x o
y 4 o o o x


after fumbling around the above is what i came up with but not sure if it's right. and i don;t know how to get the elements of R. i found those in the back of the book in the answer section for a previous question.

ok so that is totally wrong, to find my set i need to have 2 number's and that's any 2 numbers that when subtracted and then divied by 3 has no remander, so the set i came up with is (13,1)(14,2)(15,3)(16,4)(17,5) 13-1 = 12 / 3 = 4. now i have to determine if this set is reflexive symmetric,antisymmertic,transitive, and or partial order.

does anyone know and if you do can you explain how you figured it out.

Every integer has remainder, when divided by 3, of 0, 1, or 2. It should be easy to see that two numbers, x and y, have x- y divisible by 3 if and only if they have the same remainder when divided by 3. One equivalence class is {0, 3, -3, 6, -6, ...}, the multiples of 3. Another is {1, -2, 4, -5, 7, -8, ...}, numbers that have remainder 1 when divided by 3. The last equivalence class is {2, -1, 5, -4, 8, -7, 11, -10, ...}, numbers that have remainder 2 when divided by 3.

The ordered pairs are any pairs of numbers from one of those three sets.

Originally Posted by HallsofIvy

Every integer has remainder, when divided by 3, of 0, 1, or 2. It should be easy to see that two numbers, x and y, have x- y divisible by 3 if and only if they have the same remainder when divided by 3. One equivalence class is {0, 3, -3, 6, -6, ...}, the multiples of 3. Another is {1, -2, 4, -5, 7, -8, ...}, numbers that have remainder 1 when divided by 3. The last equivalence class is {2, -1, 5, -4, 8, -7, 11, -10, ...}, numbers that have remainder 2 when divided by 3.

The ordered pairs are any pairs of numbers from one of those three sets.

well according to my discreate math professor the set i put up was correct, and the problem says "determine whether each relation defined on the set of positive intergers"
there can't be negatives in the set so i don;t think those sets are correct.

final answer

determine whether each relation defined on the set of positive intergers is reflexivem symmetric,antisymmertic,transitive, and or partial order.

(x,y)∈r if 3 divides x-y

To do this we need to figure out the elements of R so we can get our ordered pair. Those elements are (13,1)(14,2)(15,3)(16,4)(17,5) with this ordered pair we can fill in our matrix. From the matrix we can see that this is a refelxive relation.
y y y y y y
X 1 2 3 4 5
X 13 X O O O O
X 14 O X O O O
X 15 O O X O O
X 16 O O O X O
X 17 O O O O X

Originally Posted by madmilitia

(x,y)∈r if 3 divides x-y

To do this we need to figure out the elements of R

First, don't mix lowercase r and uppercase R. In mathematics, lowercase and uppercase letters often denote different entities.

Originally Posted by madmilitia

so we can get our ordered pair.

Which pair? This is the same as saying, "We need to find all students who take this course so that we can find this person."

Originally Posted by madmilitia

Those elements are (13,1)(14,2)(15,3)(16,4)(17,5)

Hmm, no (1, 13), (2, 14), (4, 1), (6, 6) and infinitely many other pairs?

Originally Posted by madmilitia

with this ordered pair we can fill in our matrix.

You listed 5 pairs and then are saying, "With this ordered pair." Does this make sense?

Originally Posted by madmilitia

From the matrix we can see that this is a refelxive relation.
y y y y y y
X 1 2 3 4 5
X 13 X O O O O
X 14 O X O O O
X 15 O O X O O
X 16 O O O X O
X 17 O O O O X

A relation is reflexive when every element is related to itself. Is 1 related to itself or is it related only to 13?

well im not sure what to tell you but i did it right according to my professor, i'm pretty sure an ordered pair is more the one pair.

Originally Posted by madmilitia

i'm pretty sure an ordered pair is more the one pair.

I don't even know how to understand this. Do you mean that an ordered pair consists of several unordered pairs?