Exercise A

Identify which variables are bound and which are free.

1. $\exists x\,L(\underline{x},\overline{y})\wedge\forall y\,L(\underline{y},\overline{x})$

2. $\forall x\,A(\underline{x})\wedge B(\overline{x})$

3. $\forall x(A(\underline{x})\wedge B(\underline{x}))\wedge\forall y(C(\overline{x})\wedge D(\underline{y}))$

4. $\forall x\exists y[R(\underline{x},\underline{y})\rightarrow(J(\overline{z})\wedge K(\underline{x}))]\vee R(\overline{y},\overline{x})$

5. $\forall x_{1}(M(\overline{x_{2}})\leftrightarrow L(\overline{x_{2}},\underline{x_{1}}))\wedge\exists x_{2}\,L(\overline{x_{3}},\underline{x_{2}})$