Rita, José, and Sônia are teachers of Literature, Chemistry, and Mathematics in the cities of Palmas, Fortaleza, and Vitória, not necessarily in this order of subjects and cities. It is known that:

- José is a teacher of Literature.
- The person who works in Palmas is a teacher of Chemistry.
- Rita does not work in Vitória, nor does she teach Chemistry.

a) Who teaches Mathematics?

b) Who teaches Chemistry?

c) Who works in Vitória?
Solution

Let's build tables and interpret each of the propositions.

|  | Subject | City | Proposition |
| :---: | :---: | :---: | :--- |
| Rita | $\not$ Q M | P F V |  |
| José | L Ø M | P F V | José is a Literature teacher. |
| Sônia | $L$ Q M | P F V |  |

Since José is the Literature teacher, the others cannot teach it.

|  | Subject | City | Proposition |
| :---: | :---: | :---: | :--- |
| Rita | $\not \varnothing$ M | P F $X$ | Rita does not work in Vitória, nor does she teach Chemistry. |
| José | L $\varnothing M$ | P F V | José is a Literature teacher. |
| Sônia | $\angle$ Q M | P F V |  |

a) Rita then teaches Mathematics.

b) Sônia teaches Chemistry (and works in Palmas).

|  | Subject | City | Proposition |
| :---: | :---: | :---: | :---: |
| Rita | $L \varnothing \mathrm{M}$ | $\not P \mathrm{~F} X$ | Rita does not work in Vitória, nor does she teach Chemistry. |
| José | $\mathrm{L} \varnothing M$ | $\not P \mathrm{FV}$ | José is a Literature teacher. |
| Sônia | $\angle \mathrm{Q} M$ | $\mathrm{P} F X$ | Whoever works in Palmas is a Chemistry teacher. |

c) Therefore, Rita works in Fortaleza and José in Vitória.

|  | Subject | City | Conclusion |
| :---: | :---: | :---: | :--- |
| Rita | $\not \varnothing \mathrm{M}$ | $\not P \mathrm{~F} \not$ | Rita teaches Mathematics in Fortaleza. |
| José | $\mathrm{L} \not M$ | $\not P F^{F} \mathrm{~V}$ | José teaches Literature in Vitória. |
| Sônia | $\not \mathrm{Q} M$ | $\mathrm{P} \not F^{\prime} \not$ | Sônia teaches Chemistry in Palmas. |