Question

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}

Answer 1

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\[b\in B\]

Answer 2

So pick any element in A.

Answer 3

@theEric so the answer is A

Answer 4

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

Answer 5

I meant \[A \times B\], sorry!

Answer 6

Pick any element in A.

Answer 7

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

Answer 8

@theEric so then whats the answer

Answer 9

I want you to understand it.

Answer 10

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

Answer 11

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

Answer 12

:)

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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?