5. Ambiguity of "formulas"

a. Without the proper parenthesis, it is unclear in which order the formula should be conducted.

((ϕ∧ψ)∨θ) is read as θ and either ϕ or ψ, so either θ ϕ or θ and ψ

(ϕ∧(ψ∨θ)) is read as ϕ or ψ and θ

These are two different answers.

b. Unique readability means that a statement is clear enough that anyone reading it would arrive to the same conclusion.

c. Without a complete WFF it is unclear what operation is being performed.

∀x(x = y) is a complete WFF with ∀x as an initial segment. If a mathematician was given simply ∀x, they would not arrive at the same conclusion as one given the full WFF. Therefore, complete WFF satisfy the conditions for unique readability.

6. A^{B} is rational.

We know that $\sqrt{2}$ is irrational. So, if A=$\sqrt{2}$ and B =$\sqrt{2}$ satisfy the theorem, then we are done. If they do not, then $\sqrt{2}$^{$\sqrt{2}$} is irrational, so let a be this number. Then, letting B=$\sqrt{2}$, it is easy to verify that a^{B} = 2 which is rational and hence would satisfy the theorem.

($\sqrt{2}$^{$\sqrt{2}$})^{$\sqrt{2}$} = $\sqrt{2}$^{$2$} = 2