Question

Math proof help, please! Relations and subsets involved. I don't see the solution!

My math book proved that if sets \[A, B,C,D\] existed such that \[A \subseteq C \]and\[B \subseteq D\] then \[(A \times B) \subseteq (C \times D)\]

I need to show that the converse of that is false. I think the converse is\[(A \times B) \subseteq (C \times D)\]implies\[A \subseteq C \]and\[B \subseteq D\].
But I can't understand how it is false for some group of sets \[A,B,C,D\].

Answer 1

Use null sets :)

Answer 2

Alright, thanks.. I never went into writing a proof on that, but I thought about it and didn't see it working... Thank you!

Answer 3

No problem :)

Answer 4

Ah!! I think I finally see it.. Thanks for making me concentrate more on the null set issue!

Answer 5

Woo!

Answer 6

Got it? :)