Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Statement and Negation of Statement


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.

How Beautiful!

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 ‘ \sim {\text{P}}’.
  • While forming the negation of a statement, phrases like, ‘It is not the case’ or ‘It is false that’ are also used.
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