## ilovenyc 2 years ago Let A = {red, blue} and let B = {3, 4, 5}. Find A X B. A) {red, blue, 3, 4, 5} B) {(red, 3), (red, 4), (red, 5), (blue, 3), (blue, 4), (blue, 5)} C) { } D) {red, blue}

1. theEric

Relations aren't that hard to get, actually! I suppose you know that all the elements of $A \times B$ are coordinate pairs, such as $(a,b)$. Specifically, $a$ is an element in $A$. I mean, $a \in A$. And $b$ is an element in $B$. I mean, $b \in B$. When you try to find $A \times B$ you want to create all the ordered pairs that exist, as long as they satisify what I just said, where$a \in A$and$b\in B$

2. theEric

So pick any element in A.

3. ilovenyc

@theEric so the answer is A

4. theEric

Not quite! When you think of $AxB$, you have to think a coordinate pair like $(somethingFromA, somethingFromB)$

5. theEric

I meant $A \times B$, sorry!

6. theEric

Pick any element in A.

7. theEric

Actually, for this multiple choice question, all you need to know is that $A \times B$ has elements and they are coordinate pairs...

8. ilovenyc

@theEric so then whats the answer

9. theEric

I want you to understand it.

10. theEric

I'm imposing my view upon you, I know.. But understanding things like this will be essential to understanding things later.

11. theEric

I'm willing to walk you through a similar problem.

12. theEric

:)

13. theEric

$(a \in A, b \in B)$ Example:$(red,3)$

14. ilovenyc

@theEric okay I did the work, and I came up with B, am i right?

15. theEric

$red \in A$and$3 \in B$so $(red,3)$is one of those ordered pairs in $A \times B$.

16. theEric

If you understand that last thing I said, you'll know whether you have the answer or not! If you understand "relations" you'll know what set would have to be the relation. Would you like a hand with anything?