# Thread: intersecting relationship with set

1. ## intersecting relationship with set

The relation R on Z is defined by (x,y) in R if and only if x-y is even. Write $\displaystyle R \cap (\{1,2,3\}x\{1,2,3\})$ as a set by listing its elements.

The $\displaystyle \cap$ confuses me. Is the question asking which elements of the given set are in R? Then that would be $\displaystyle (\{1,1\},\{2,2\},\{3,3\},\{1,3\})$.

2. ## Re: intersecting relationship with set

Originally Posted by Jskid
The relation R on Z is defined by (x,y) in R if and only if x-y is even. Write $\displaystyle R \cap (\{1,2,3\}\times\{1,2,3\})$ as a set by listing its elements.
The $\displaystyle \cap$ confuses me. Is the question asking which elements of the given set are in R? Then that would be $\displaystyle (\{1,1\},\{2,2\},\{3,3\},\{1,3\})$.
That is the correct idea.
However, it should be written as $\displaystyle \{(1,1),~(2,2),~(3,3),~(1,3),\}$.
Relations are sets of pairs.

3. ## Re: intersecting relationship with set

Note the last comma that Plato left as a hint.

4. ## Re: intersecting relationship with set

Does order matter? For example is (1,3) different than (3,1)?

5. ## Re: intersecting relationship with set

Of course the order matters. If you have ever read about unrequited love, you should know.

6. ## Re: intersecting relationship with set

Originally Posted by emakarov
Of course the order matters. If you have ever read about unrequited love, you should know.
I think I misunderstood my prof. Order doesn't matter when {(1,2),(3,4)}={(3,4),(1,2)} right?

Someone told me parentheses are just for holding things together but how is that different than curly braces?

7. ## Re: intersecting relationship with set

order doesn't matter in listing set elements. it DOES matter in listing ordered pairs (note the "ordered" in ordered pair).

the ordered pair (a,b) is not, in general, the same pair as (b,a).

for example, if R is the relation <, then (3,4) is in R, but (4,3) is NOT.

8. ## Re: intersecting relationship with set

Originally Posted by Jskid
I think I misunderstood my prof. Order doesn't matter when {(1,2),(3,4)}={(3,4),(1,2)} right?
Someone told me parentheses are just for holding things together but how is that different than curly braces?
A relation on a set is subset of the cross product of the set with itself.
That means that relations are sets of ordered pairs.
Note the word ordered.
$\displaystyle (1,2)\ne (2,1)$ but $\displaystyle \{1,2\}=\{2,1\}$
So you are correct $\displaystyle \{(1,2),(3,4)\}=\{(3,4),(1,2)\}$
BUT $\displaystyle \{(1,2),(4,3)\}\ne\{(3,4),(1,2)\}$.