Set Relation Question | PDF Guide

[dimitri151]

See attached pdf.

 

[chiro]

Hi there.

I'm a little confused with the notation. Does A_k B_k mean the cartesian product between A_k and B_k?

 

[dimitri151]

No, it means the intersection (sorry I'm using a mix of new notation and an old style notation where the intersection of two sets is shown as multiplication and the union is like addition).

 

[chiro]

No, it means the intersection (sorry I'm using a mix of new notation and an old style notation where the intersection of two sets is shown as multiplication and the union is like addition).

Just looking at the relationship adding up C_complement and C together give the union of all 'A's for index 1 to n which also give the 'universe' and the context for the sets A_k and B_k

Have you been given any other information about the context of the sets? Is each set meant to be disjoint from one another?

You've probably done this but typically what comes to mind in negation questions is to use De-Morgans theorems and the theorems of set algebra, collect terms, simplify etc, but yeah I can see why this is tripping you up.

Hopefully it gives a few more constraints that can be used to simplify the problem because personally I think you need more information to solve it, but I could be wrong.

 

[dimitri151]

Thank you for the reply. Of course I tried Demorgans laws. The theorem is a really great theorem otherwise I wouldn't waste so much time on it. I'll post it verbatim when I get the chance. Your suggestion is helpful because it shows that the union of the A_k's equals the universe. I think that's one of the statements in the theorem to be proved.