What is the difference between tautology and contradiction

Consider a statement like:. That statement is a tautology, and it has a particular form, which can be represented symbolically like this:. That statement is a contradiction, and it has a particular form, which can be represented symbolically like this:. That statement is a contingent statement.

Instead, its truth depends on the way the world is. Suppose that Matt is 39 years old. In that case, the statement is true. But suppose he is 37 years old. Statements 1 — 13 are basic properties, while 14 — 22 can be considered additional laws. The following theorem lists some useful contradictions, and again, the proof requires construction of the appropriate truth tables and is left to the exercises.

You should be aware that the list of possible tautologies and contradictions we could have chosen is virtually endless. We have simply chosen those which will be of most benefit to us later. As a final example we will provide the following example of a truth table involving three statements. The following truth table Table 1.

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