# Is this valid notation?

Is this valid notation?
$$\left\{(a,b) \in \mathbb{R}^2 \;\middle|\; \left(a=6+|b|, |b|\le4\right) \ \text { or } \ \left(|a|\le3, |b|=2\right) \right\}$$

How to graph it, please? thanks

It's the result of a problem, but I'm not sure this is a correct way to write it or how to graph the set.

• The question has no context. So I think that the most difficult part is how to plot $|a|+|b|=6.$ See wolframalpha.com/input/?i=plot+%7Cx%7C%2B%7Cy%7C%3D6
– mfl
Feb 17, 2019 at 18:04
• what do you mean by context? It's a direct question. Either this is a sensible set or it's not, and if it's sensible then it should be plottable.
– Loli
Feb 17, 2019 at 18:09
• By context I mean: What do you know about the question? What have you tried? Where are you stuck?
– mfl
Feb 17, 2019 at 18:16
• @mfl can you at least say if the notation makes sense? i'll keep working on the rest myself.
– Loli
Feb 17, 2019 at 18:19
• The set is correctly written.
– mfl
Feb 17, 2019 at 18:20

The way you have written is fine, but it's probably nicer to write it as $$\{ (x,y) \ | \ y \in [-4,4], |x| + |y| = 6 \} \cup \ \big( \ [-3,3] \times \{ -2,2 \} \ \big).$$