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| Tautologies |
Tautologies
Definition
In logic, a tautology is a statement that is true in every possible case. The opposite of a tautology is a contradiction, a statement being false in every possible cases.
Example
| p | q | p OR q | p → p OR q |
|---|---|---|---|
| T | T | T | T |
| T | F | T | T |
| F | T | T | T |
| F | F | F | T |
As we can see in the truth table, the statement "p → p OR q" is always true (see last column).
An example in terms of Boolean logic is B || !B. It is always true that B is true or B is not true.
The opposite of a tautology is a contradiction, a formula which is "always false". In other words, a contradiction is false for every assignment of truth values to its simple components.
An example of a contradiction with Boolean logic is B && !B. It is impossible for B to be both true and false at the same time.
Note
The arrow simply means "implies". p implies p OR q, it can also mean if...then...
More Information:
Wikipedia Tautology (Logic) Youtube Truth Tables Wikipedia Logic Symbols