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.

QUESTION

Miscellaneous Exercise 1 | Q 4.12 | Page 33

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.