Question

your answer is incorrect. which of the following statements is false? a) if m and n are both real numbers, then m + n is also a real number. b) if m is real number, then m × 1 = m. c) between any pair of rational numbers, there is at least one rational number. d) between two consecutive natural numbers, there is at least one natural number. e) if m and n are both real numbers, then m + n = n + m. f) none of the above.

Explanation:

• Option a: The set of real numbers is closed under addition, so if \( m \) and \( n \) are real, \( m + n \) is real. This is true.
• Option b: Multiplicative identity property states \( m\times1 = m \) for any real \( m \). This is true.
• Option c: The set of rational numbers is dense, meaning between any two rational numbers, there is another rational number. This is true.
• Option d: Consecutive natural numbers (e.g., 2 and 3) have no natural number between them. So this statement is false.
• Option e: This is incorrect as option d is false.

Answer:

d. Between two consecutive natural numbers, there is at least one natural number.