How to go about sketching this subset of $R^2$

Question

If we let $X = \{(x,y) \in R^2 : |x| + |y| \ge 1, \max\{|x|,|y|\} \le 1\}$ how would I go about sketching this subset, I am having some trouble getting started.

Answer 1

Hint: The curves $\max\{|x|,|y|\} = 1$ and $|x| + |y| = 1$ will form the boundary of the region that you're trying to sketch. You should find that both of these curves are squares in the $xy$-plane (though the second is a "tilted" square).