Logical Statement Math Example 3

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

Example 3

easy
Determine the truth value of each: (a) 77 is a prime number. (b) 00 is a natural number. (c) Every square is a rectangle.

Solution

  1. 1
    (a) 7 has no divisors other than 1 and itself, so this is true.
  2. 2
    (b) By the convention that N={0,1,2,…}\mathbb{N} = \{0,1,2,\ldots\}, this is true (note: some conventions exclude 0).
  3. 3
    (c) A square has four right angles and opposite sides equal, meeting the definition of a rectangle. True.

Answer

(a) True, (b) True (by convention), (c) True\text{(a) True, (b) True (by convention), (c) True}
Evaluating statements requires checking definitions carefully. Some statements depend on the convention used.

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 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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