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.

  • $\begingroup$ 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 $\endgroup$
    – mfl
    Feb 17, 2019 at 18:04
  • $\begingroup$ 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. $\endgroup$
    – Loli
    Feb 17, 2019 at 18:09
  • $\begingroup$ By context I mean: What do you know about the question? What have you tried? Where are you stuck? $\endgroup$
    – mfl
    Feb 17, 2019 at 18:16
  • $\begingroup$ @mfl can you at least say if the notation makes sense? i'll keep working on the rest myself. $\endgroup$
    – Loli
    Feb 17, 2019 at 18:19
  • $\begingroup$ The set is correctly written. $\endgroup$
    – mfl
    Feb 17, 2019 at 18:20

1 Answer 1


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

You can see here (thanks to @mfl) what the first set in the union looks like. The second is just two horizontal lines.

If you lay these on top of each other, then you get what you're looking for.


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