YALMIP
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Convex graph models should be sufficient in some logic or models
This should be able to represent the components of the second set using no binary variables
x = sdpvar(2,1);
plot([-10 <= x <= 10, ([abs(x-1) <= 1, abs(x-1)>=0.1] | (norm(x-2,1) <= 1)),x],x)