# Propositional Forms

A Tautology:

Is a Propositional form whose truth value is true for all possible values of its propositional variables.

P v not P

For this compound expression to be false, both P or not P must be false. But this is impossible, because when P is true, not P will false and visa versa.

P = The Car is Red

P v not P = The Car is Red or The Car is Not Red.

If you draw up a truth table where a column has all True Values in one column, then you have a tautology for the compound expression of that column.

Consider (P ^ Q) => P

Notice not only the column of the compound expression is all true, but also one entire row.

Is a Propositional form which is always false.

P ^ not P

For this compound expression to be true, both P and not P must be true. But this is impossible, because when P is true, not P will false and visa versa.

P = The Car drives.

P ^ not P = The Car Drives and The Car does not drive.

If you draw up a truth table where a column has all False Values in one column, then you have a contradiction for the compound expression of that column.

A Contingency

is a Propositional form which is neither a Contradiction or a Tautology.