$($b$)$ v Kz$)$

$($c$),($Ex$)(Cyv(FxGa))$

Expanding a wff is not the same as rewriting the wff in conjunctive normal form $($or rewriting it in disjunctive normal form$).$ Read the text and my handout on how

to do an expansion.

For the following wffs$,$ indicate which variables are free and which are bound $($you can use $\text{'}F\text{'}$ for free and $\text{'}B\text{'}$ for bound.$)$ Make sure you draw a vertical line

underneath each variable with the letters $\text{'}F\text{'}$ or $\text{'}$B$\text{'}$ at the bottom of each vertical line. Make sure you know what is and what is not a variable. Not every symbol in

the language of predicate logic is a variable. The reading $($Scope$,$ binding, expansions$)$ lists the symbols that are variables and the symbols that are names $($i$.$e$.,$

individual constants$).$ Names are not variables.

You can write the wffs with the vertical lines on a piece of paper and submit a photo of it$.$

Instead of using vertical lines and F$/$B$,$ you can color the bound variables red and the free variables green. Example:

$($x$)(($Fx & Gx$)$ sup Kxyw$)$

$($a$)($x$)($y$)($z$)(($Fxyd sup Gxyb$)v(HxvasupHzbu))$

$($b$)($Ex$)($Ey$)$ Hxxay sup $($z$)($Ex$)($Gfzy v Hyyx$)$

$($c$)($z$)($Ex$)($y$)($Axayzw v Bxyffcuvz$)$