Page 6 - LESSON NOTE
P. 6
Validate by contradiction
We assume that p is not true i.e. ∼p is true. Then, we arrive at some result which contradicts
our assumption. Therefore, we conclude that p is true.
Examples
1. Which of the following sentences are statements? Give reasons for your answer.
(i) There are 35 days in a month.
(ii) Mathematics is difficult.
(iii) The sum of 5 and 7 is greater than 10.
Answer:
(i) This sentence is incorrect because the maximum number of days in a month is 31.
Hence, it is a statement.
(ii) This sentence is subjective in the sense that for some people, mathematics can be easy
and for some others, it can be difficult. Hence, it is not a statement.
(iii) The sum of 5 and 7 is 12, which is greater than 10. Therefore, this sentence is always
correct. Hence, it is a statement.
2. Write the negation of the following statements:
(i) Chennai is the capital of Tamil Nadu.
(ii) √2 is not a complex number.
Answer:
(i) Chennai is not the capital of Tamil Nadu.
(ii) √2 is a complex number.
