1. ## Functions and Relations

I'am having problems understanding what this means?

Let C=D ={-3,-2,-1,1,2,3} and defione a relation S from C to D as follows For all (X,Y) set of C x D

(x,y) set of S means that 1/x -1/y is an integer?

Is 2 S 2.

This is only first part of what its asks because I want to be able to do the rest by myself but if somone could please help me understand this part.

Thanks

2. Originally Posted by Thetheorycase
I'am having problems understanding what this means?

Let C=D ={-3,-2,-1,1,2,3} and defione a relation S from C to D as follows For all (X,Y) set of C x D

(x,y) set of S means that 1/x -1/y is an integer?

Is 2 S 2.

This is only first part of what its asks because I want to be able to do the rest by myself but if somone could please help me understand this part.

Thanks
To state a little more clearly, define relation S such that x S y if and only if 1/x - 1/y is an integer.

So, is 1/2 - 1/2 an integer?

3. defione a relation S from C to D as follows For all (X,Y) set of C x D

(x,y) set of S means that 1/x -1/y is an integer
If I understand you right, $\displaystyle (x,y)\in S$ iff $\displaystyle 1/x-1/y$ is an integer for all $\displaystyle (x,y)\in C\times D$. The question then asks if $\displaystyle 2\mathrel{S}2$, i.e., if 2 is related to 2 by $\displaystyle S$.

Well, this happens, by definition, if $\displaystyle (2,2)\in S$.

Hint: if you can't write the symbol $\displaystyle \in$, you can just say "in". For example, $\displaystyle (x,y)$ in $\displaystyle S$.

4. Thanks Undesinded and Emakarov

So 2S2 is 0 which is an integer so Yes

-1S-1 ---> -1/1 + 1/1 = 0 so yes

is (3,3) in S ---> 1/3 - 1/3 = 0 so yes

is (3, -3) in S ----> 1/3 + 1/3 = 2/3 no

5. Is $\displaystyle (2,-2)\in S?$

Is $\displaystyle (-2,2)\in S?$

6. Is (2, -2) in S? ---> 1/2 +1/2 = 2/2 = 1 yes

Is (-2, 2) in S ----> -1/2 - 1/2 = -2/2 = -1 yes

7. Originally Posted by Thetheorycase
So 2S2 is 0...
Might help to clear up right now that saying "2S2 is 0" is incorrect use of terms.

2S2 is either true or false. Think of S the way you would think of other relations that you are familiar with and have used many times: =, <, >, etc.

4 = 5 is false but 4 < 5 is true.

4 is not related to 5 by =, but 4 is related to 5 by <.

1/x - 1/y is just a value used to determine whether xSy is true or false, but it is not the value of xSy.

Also note that in general it's not always the case that a relation is symmetric. "x is related to y" is not necessarily the same as "y is related to x". You can compare "x is less than y" with "y is less than x".

8. Thanks for the tip
Originally Posted by undefined
Might help to clear up right now that saying "2S2 is 0" is incorrect use of terms.

2S2 is either true or false. Think of S the way you would think of other relations that you are familiar with and have used many times: =, <, >, etc.

4 = 5 is false but 4 < 5 is true.

4 is not related to 5 by =, but 4 is related to 5 by <.

1/x - 1/y is just a value used to determine whether xSy is true or false, but it is not the value of xSy.

Also note that in general it's not always the case that a relation is symmetric. "x is related to y" is not necessarily the same as "y is related to x". You can compare "x is less than y" with "y is less than x".