Question

A = {1,2} B = {1,2,3} find the set A x B

is the answer:
AxB = {{1},{1,2},{1,3},{2},{2,3}} ?

Answer 1

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Answer 2

I believe this is for the Cartesian product?

In general... if \(a\) is an element of \(A\) and \(b\) is an element of \(B\), then the Cartesian product \(A \times B\) is:
\[ A\times B=\{ (a,b) \mid a \in A \text{ and }b\in B\}\]
So take every element of A and associate it with each element of B. It's important to know that the order of the pair \((a,b)\) matters, because \(B \times A\) gives the set all of pairs \((b, a)\) instead, and this is NOT the same!

Answer 3

You can think of the Cartesian product where A represents the x-axis and B represents the y-axis, and you find all coordinates that encompass the "rectangle" formed by A and B: