The basic unit involved in mathematical reasoning is a mathematical statement.
- A sentence is called a “mathematically acceptable” statement if it is either true or false but not both.
- Statement is also called ‘preposition”.
- The sum of x & y is greater than 0.
Open the door.
Where are you going?
The above sentence are not statement in mathematical language.
- If a sentence immediately decide is it true or false, then this is acceptable statement, but if it show confusion rather than true or false, is not acceptable as a statement in mathematics.
- Sentence involving variable time such as “today”, “tomorrow”, or “yesterday” are not statements.
Negation of a Statement
The denial of a statement is called the negation of the statement.
Example – New Delhi is a city.
The negation of this statement is New Delhi is not a city.
- If P is a statement, then negation of P is also a statement & is denoted by ‘’.
- While forming the negation of a statement, phrases like, ‘It is not the case’ or ‘It is false that’ are also used.