1. ## recursive definition

Hi
I have a problem which i couldn't solve
could somebody help me

1. Give a recursive definition of the length of a well formed formula, that is of the number of symbols occuring in it . for example the length of (p ^ (¬q)) is 8.

2. show that there is no well formed formula of length 2,3 and 6 , but any other positive length is possible

Please respond as soon as possible

2. Hello,

1) The length of an atom is 1.
2)a) If the length of w is n, the length of (w) is n+2.
2)b) If the length of w_1 is n_1 and the length of w_2 is n_2, the length of w_1^2w_2 is n_1+n_2+1.
2)c)...etc.

For the second problem, use the results of the first one.

Bye.