Logical Statement Math Example 4

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

Example 4

easy
Which of the following are logical statements: (a) '77 is prime', (b) 'Open the window', (c) 'What is 2+52+5?', (d) '32=103^2 = 10'?

Solution

  1. 1
    A logical statement must be a declarative sentence with a definite truth value. So (a) is a statement and it is true; (d) is a statement and it is false.
  2. 2
    A command and a question do not have truth values, so (b) and (c) are not logical statements.

Answer

(a)Ā andĀ (d)Ā areĀ logicalĀ statements;Ā (b)Ā andĀ (c)Ā areĀ not.(a) \text{ and } (d) \text{ are logical statements; } (b) \text{ and } (c) \text{ are not.}
Truth value is what matters. A sentence can be a valid logical statement even when it is false, but questions and commands are not statements because they are neither true nor false.

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 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 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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