solution

1. \(A(x)\coloneqq [\text{$x$ is a vowel}]\) makes it true; \(A(x)\coloneqq [\text{$x$ is a consonant}]\) makes it false.

2. \(A(x)\coloneqq [\text{$x$ is a consonat}]\) is a solution of \(\exists x : A(x)\). but \(A(x)\coloneqq [\text{$x$ is $v$}]\) is not.

3. \([\text{$x$ is below $i$}]\) for true and \([\text{$x$ is above $a$}]\) for false.

   For the second part of the exercise we find:

   \[ \begin{equation}\begin{split}&\forall x \in \{a,b,c\}:\exists ! y\in \{x,y\}\in F\\&\iff\\&\left(((a,1)\in F)\dot{\lor}((a,2)\in F)\right) \land \left(((b,1)\in F)\dot{\lor}((a,2)\in F)\right)\land\left(((c,1)\in F)\dot{\lor}((c,2)\in F)\right)\end{split}\end{equation} \]

   The true values are: (1) True, (2) True, (3) False, (4) True