Negating a statement, quick check.

[malicx]

Homework Statement

So, I have a set
$$S = (x, y) \in \mathbb{R} | (x and y \in \mathbb{Q}) or (x and y \notin \mathbb{Q})$$

I want to find
$$T = \mathbb{R} minus S$$

so I am negating this and get


$$T = (x, y) \in \mathbb{R} | (x or y \in \mathbb{Q}) and (x or y \notin \mathbb{Q})$$

which really just means that one coordinate must be rational, and the other must be irrational. Is this correct?

Thanks. I also seem to be having problems in latex getting the set complement R\S and brackets around my sets working, so sorry about that.

 

[micromass]

This seems ok!

 

[Outlined]

yes this is correct, it follows from elementary rules of logic