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Question
What is tautology? What is contradiction?
Show that the negation of a tautology is a contradiction and the negation of a contradiction is a tautology.
Solution
- Tautology:
A statement pattern having truth value always T, irrespective of the truth values of its component statement is called a tautology. - Contradiction:
A statement pattern having truth value always F, irrespective of the truth values of its component statement is called a contradiction.
Let Statement p tautology. Consider, truth table
| p | ~ p |
| T | F |
i.e., negation of tautology is contradiction.
Let statement of contradiction. Consider, truth table
| q | ~ q |
| F | T |
i.e., negation of contradiction is tautology.
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