#### 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.