Logical Statement Math Example 5

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Example 5

medium
Classify each as a statement or not: (a) '7+3=117 + 3 = 11' (b) 'Is 5 prime?' (c) 'Every square is a rectangle.'

Solution

  1. 1
    A logical statement is a declarative sentence that is either true or false (has a definite truth value).
  2. 2
    (a) '7+3=117 + 3 = 11' is a declarative sentence. Since 7+3=10≠117 + 3 = 10 \neq 11, it is false — but it is still a statement.
  3. 3
    (b) 'Is 5 prime?' is an interrogative sentence (a question). Questions do not have truth values, so this is NOT a statement.
  4. 4
    (c) 'Every square is a rectangle.' is a declarative sentence. Since all squares satisfy the definition of a rectangle, it is true — it is a statement.

Answer

(a) Statement (false)(b) Not a statement(c) Statement (true)(a) \text{ Statement (false)} \quad (b) \text{ Not a statement} \quad (c) \text{ Statement (true)}
A sentence qualifies as a logical statement if and only if it is declarative and has a definite truth value. Questions, commands, and exclamations are not logical statements, even if they involve mathematical content.

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).

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More Logical Statement Examples

Example 1 easy

Classify each as a statement (proposition) or not: (a) [formula] (b) 'Close the door.' (c) [formula]

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)

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