Merge branch 'patch-1' into 'master'

Correct a mistake

See merge request etienne.levecque.etu/foundations-of-databases-exercise-corrections!3

Chapter 4/Exercise-4.4.md

@@ -20,10 +20,12 @@ free variables** and, for each **I** over **R** and valuation $`ν`$ over free(
 
 Let's say that : $`\Psi = \Phi \ \varphi \ \Phi^{\prime}`$ . In that case $`\Psi^{\prime} = \Phi \ \psi \ \Phi^{\prime}`$.
 
-$`\blacksquare`$ Clearly, $`free(\Psi)=free(\varphi) \ \text{and} \ free(\Psi^{\prime})=free(\psi)`$
+$`\blacksquare`$ Clearly, $`free(\Psi)=free(\Phi) \cup free(\varphi) \cup free(\Phi^{\prime}) \ \text{and} \ free(\Psi^{\prime})= free(\Phi) \cup free(\psi) \cup free(\Phi^{\prime})`$
 By hypothesis, $`\varphi`$ and $`\psi`$ are equivalent and so :
 
-$`free(\Psi)=free(\varphi)=free(\psi)=free(\Psi^{\prime})`$
+$`free(\varphi)=free(\psi)`$
+
+Hence, $`free(\Psi)=free(\Psi^{\prime})`$
 
 $`\blacksquare`$  Let's **I** an instance over **R** and $`v`$ a valuation over $`free(\Psi)=free(\Psi^{\prime})`$.