# Statement, Negation

How to solve the truth values of a statement and its negation problems: examples and their solutions.

## Example 1

A statement is a sentence that is either true or false.*p*: 5 is a positive number.

The truth value of *p* is true.

~*p* is called 'not *p*'.

So *p* and ~*p* have the opposite truth values.

~*p*: 5 is **not** a positive number.*p* is true.

So ~*p* is false.

~(~*p*) has two ' ~ '.

So just like -(-*p*) = +*p*,

~(~*p*) = *p*.

~(~*p*) = *p*: 5 is a positive number.*p* is true.

So ~(~*p*) is true.

## Example 2

*p*: 1 + 1 = 3*p* is false.

~*p*: 1 + 1 **≠** 3*p* is false.

So ~*p* is true.

~(~*p*) = *p*: 1 + 1 = 3*p* is false.

So ~(~*p*) is false.