Logical Statement Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Classify each as a statement (proposition) or not: (a) 3+5=83 + 5 = 8 (b) 'Close the door.' (c) x>2x > 2.

Solution

  1. 1
    (a) 3+5=83 + 5 = 8 is a declarative sentence that is true. It is a statement.
  2. 2
    (b) 'Close the door' is a command, not declarative. It is not a statement.
  3. 3
    (c) x>2x > 2 has an unspecified variable, so its truth value is undetermined. It is an open sentence, not a statement.

Answer

(a)Ā StatementĀ (true),Ā (b)Ā NotĀ aĀ statement,Ā (c)Ā NotĀ aĀ statementĀ (openĀ sentence)\text{(a) Statement (true), (b) Not a statement, (c) Not a statement (open sentence)}
A logical statement must be a declarative sentence with a definite truth valueā€”either true or false, not both and not indeterminate.

About Logical Statement

A logical statement (or proposition) is a declarative sentence that has exactly one truth value: it is either true or false. For example, '7 is prime' is a logical statement (true), while 'Is 7 prime?' is not (it's a question).

Learn more about Logical Statement ā†’

More Logical Statement Examples

Example 2 medium

Negate the statement: 'All prime numbers are odd.'

Example 3 easy

Determine the truth value of each: (a) [formula] is a prime number. (b) [formula] is a natural numbe

Example 4 easy

Which of the following are logical statements: (a) '[formula] is prime', (b) 'Open the window', (c)

Example 5 medium

Classify each as a statement or not: (a) '[formula]' (b) 'Is 5 prime?' (c) 'Every square is a rectan

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