We define a propositional formula as follows:
- {a,b,...j} are atomic propositions, representing either true or false.
- If A and B are propositional formulae, then so are:
- (A ^ B) -- ^ is boolean "and"
- (A v B) -- v is boolean "or"
- ~A -- ~ is boolean "not"
For example, ((a v b) ^ (~c v a)) is a propositional formula. A tautology is a propositional formula that equates to true for all possible value assignments to the atomic propositions. Our previous example ((a v b) ^ (~c v a)) is not a tautology because for the assignments a = false, b = false and c = true, the formula evaluates to a false. However (a v ~a) is a tautology because no matter what the atomic proposition is this equates to true; (true or not-true) == true, (false or not-false) == true.
The input file DATA5.txt will contain 5 test cases, each three lines (not more than 255 characters) with a propositional formula per line.
The output file OUT5.txt will contain 5 lines of output, each three characters long. Y for tautology, N for not tautology.
((a v b) ^ (~c v a)) (a v ~a) ~(a ^ ~a) a ~b ((a ^ b) v ~(c ^ ~c))
NYY NNY