The formal rules of logic are also tautologous when they are expressed in conditional form, as in PQCPAQC. All tautologies are equivalent--and they are also uninformative.

The opposite of a statement that is necessarily true is one that is necessarily false--a contradiction as in you are a student and you are not a student (PPNA). Keep in mind that statements can be inconsistent (unable to both be true) without being contradictory, as in saying that today is Monday while also saying today is Tuesday.

The most important tautologies are those which are our key rules in formal logic, such as the pattern in which we say that the combination of PQC and P implies Q (C elim or modus ponens).

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