Exercise 5.3
1

Can
the $xj
rule be applied in the following cases? If it can, what would the
result be? 

(i)

"x[Fxa®Gx]
$zFz


(ii)

[$xFxÚ$yGy]


(iii)


2

Each
of the following is a tableau which consists, so far, of just one
formula. What rule, if any, can be applied to the formula, and with
what result? Note that there is only ever at most one rule which
can be applied.


(i)

"x[GxaÙHxa] 

(ii) 
[$xGxa®"yFy] 

(iii) 
¬[¬$xFx®P] 

(iv) 
$x"y[Fx«Ryax] 

(v) 
"x"y"z[[RxaÙRyb]®Sxyz]] 

(vi) 
"x"y"z[[RxyÙRyz]®Sxyz]]

