WFF 'N PROOF is a logic game played with dice. Each die has six faces representing some subset of the possible symbols K, A, N, C, E, p, q, r, s, t. A Well-formed formula (WFF) is any string of these symbols obeying the following rules:
- p, q, r, s, and t are WFFs
- if w is a WFF, Nw is a WFF
- if w and x are WFFs, Kwx, Awx, Cwx, and Ewx are WFFs.
The meaning of a WFF is defined as follows:
- p, q, r, s, and t are logical variables that may take on the value 0 (false) or 1 (true).
- K, A, N, C, E mean and, or, not, implies, and equals as defined in the truth table below.
|Definitions of K, A, N, C, and E|
| w x|| Kwx|| Awx|| Nw|| Cwx|| Ewx|
| 1 1|| 1|| 1|| 0|| 1|| 1|
| 1 0|| 0|| 1|| 0|| 0|| 0|
| 0 1|| 0|| 1|| 1|| 1|| 0|
| 0 0|| 0|| 0|| 1|| 1|| 1|
is a WFF that has value 1 (true) regardless of the values of its variables. For example, ApNp
is a tautology because it is true regardless of the value of p
. On the other hand, ApNq
is not, because it has the value 0 for p=0, q=1
. You must determine whether or not a WFF is a tautology.