Set $A\subset \mathbb{R}$ so that $\lambda(A\cap [a,b])>0$ and $\lambda([a,b]\setminus A)>0$. [duplicate]

Question

Build a set $A\subset \mathbb{R}$ so that for all interval $[a,b]\subset \mathbb{R}$ meets the following two properties:

1. $\lambda(A\cap [a,b])>0$.

2. $\lambda([a,b]\setminus A)>0$$

Where $\lambda$ is Lebesgue Measure.

The true is thatI do not have any idea how to build this set A. I hope can help me. Thanks!