DWITE, December 2011, Problem 5
We define a propositional formula as follows:
- are atomic propositions, representing either true or false.
- If and are propositional formulae, then so are:
- — is boolean "and"
- — is boolean "or"
- — is boolean "not"
For example, 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 is not a tautology because for the assignments , and , the formula evaluates to a false. However 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 will contain 5 test cases, each three lines (not more than 255 characters) with a propositional formula per line.
The output 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))
~ is used for ,
^ for , and
v for .