Statement

Statements

3.1

Statements

Determine whether a sentence is a statement or not a statement.

	Definition

	A statement is a sentence of which the truth value can be determined , that is either true or false, but not both.

Questions, explanation and command sentences are not statements. (The truth values cannot be determined)

	Example

	Determine whether each of the following sentences is a statement or not. Give the reason.

	a. \(4 + 3 = 8\) (statement, it is a false statement).

	b. The Pentagon has \(5\) sides (Statement, it is a true statement).

	Tips

	Not all the mathematical statements are true. The truth values of the mathematical statements can be determined

	Example

	Determine whether the following mathematics statements are true or false. Explain if the statement is false.

	(a) \(3\) is a prime number (true statement)

	(b) \(–11 > –8\) (False statement) Because \(-8\) is bigger than \(-11\)

	(c) \(5\) is a factor to \(8\) (False statement). \(5\) cannot be a factor to \(8\). Factors of \(5\) are numbers which on dividing \(5\) leave no remainder. Since \(5\) is a prime number, it has only two factors.

Negation a statement

Use the word no or not to negate a statement
The negation of statement p is written as ~p

	Example

	Form a negation (~p) for each of the following statements (p) by using the word "no" or "not"

	(a) \(13\) is a multiple of \(5\) \(13\) is not a multiple of \(5\)

	(b) \(20\) is a prime number \(20\) is not a prime number

Determine the truth value of a compound statement

	Definition

	A compound statement is a combination of two or more statements by using the word "and" or "or".

The word "and" in a mathematical statement mean both while the word "or" means one of them or both.

	Example

	Combine the following statements, \(q\) and \(r\) by using the words "and" or "or"

	\(q\): A pentagon has two diagonals \(r\): A heptagon has four diagonals

	Solution: A pentagon has two diagonals and a heptagon has four diagonals A pentagon has two diagonals or a heptagon has four diagonals