Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 1 Mathematical Logic Exercise 1.3 [Page 7]
Write the negation of the following statement.
All men are animals.
Some men are not animals.
Write the negation of the following statement.
\(-3\) is a natural number.
\(-3\) is not a natural number.
Write the negation of the following statement.
It is false that Nagpur is capital of Maharashtra.
Nagpur is capital of Maharashtra.
Write the negation of the following statement.
\(2 + 3 \neq 5\)
\(2 + 3 = 5\)
Write the truth value of the negation of the following statement.
\(\sqrt{5}\) is an irrational number.
Truth value of the given statement is T.
∴ Truth value of its negation is F.
Write the truth value of the negation of the following statement.
London is in England.
Truth value of the given statement is T.
∴ Truth value of its negation is F.
Write the truth value of the negation of the following statement.
For every \(x \in \mathbb{N}\), \(x + 3 < 8\).
Truth value of the given statement is F. (For example, if \(x=5 \in \mathbb{N}\), then \(5+3 = 8\), which is not less than 8. If \(x=6 \in \mathbb{N}\), then \(6+3 = 9\), which is not less than 8).
∴ Truth value of its negation is T.
