Opinion on proof (cartesian product -sets)-some guidance needed

• Mar 7th 2010, 03:06 PM
gate13
Opinion on proof (cartesian product -sets)-some guidance needed
Good day to all

I have attached the question asked and my work for better legibility. I need to prove that the LHS is a proper subset of the RHS. I have (I believe) managed to proved that it is a subset of the RHS but not a proper subset. I know that to do so, I would need to prove that the LHS subset of RHS and LHS different than RHS. This is where my problem arises. Any help would be greatly appreciated.

Kindest regards
• Mar 7th 2010, 03:23 PM
Plato
Why not learn to post in LaTeX?
It almost as easy as equation editor.
$$(a,b)\in A\times B$$ gives $(a,b)\in A\times B$.

You work is correct.
• Mar 7th 2010, 03:31 PM
emakarov
I am not sure if in general this is a proper subset because each of the implication (except for the last) can be turned into an equivalence...
• Mar 7th 2010, 03:41 PM
Plato
Quote:

Originally Posted by emakarov
I am not sure if in general this is a proper subset because each of the implication (except for the last) can be turned into an equivalence...

I took that to be a typo: lack of LaTex usage.
Because clearly it need not be a proper subset.