1. Sep 24, 2008

### blackdvl666

ok guys this is from my logics course!!!!

this question may be very simple but i am just gettin stuck

give a recursive definition of the length of a well formed formula that is of the number of the symbols occuring in it. For example length of (p^(~q)) is 8.

2. Sep 24, 2008

### CompuChip

OK, so if p is an atomic formula, the length is 1.
What possibilities do you have to make a new wff out of two wffs p and q?
For example, if p is a wff of length n, then (~p) is one of length n + 3.
If p and q are wff's of length n and m, respectively, then (p^q) is of length m+n+3.