Luíza, Maria, Antônio and Júlio are siblings. Two of them have the same height. It is known that

- Luíza is taller than Antônio;
- Antônio is taller than Júlio;
- Maria is shorter than Luíza;
- Júlio is shorter than Maria.

Which of them have the same height?
(a) Maria and Júlio
(c) Antônio and Luíza
(e) Antônio and Maria
(b) Júlio and Luíza
(d) Antônio and Júlio
The correct option is (e).

We will use the notation $a\mathrm{A}$ or, equivalently, $\mathrm{A}\mathrm{J}$ or, equivalently, $\mathrm{J}<\mathrm{A}$ );

(iv) $\mathrm{J}$ is less than $\mathrm{M}(\mathrm{J}<\mathrm{M})$.

From (i) and (iii) it follows that $\mathrm{J}<\mathrm{A}<\mathrm{L}$. Therefore, the siblings of the same height are not among Júlio, Antônio, and Luíza. From (ii) and (iv) it follows that $\mathrm{J}<\mathrm{M}<\mathrm{L}$. Therefore, the siblings of the same height are not among Júlio, Maria, and Luíza. Thus, the only option is that Antônio and Maria have the same height.