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Difficulty: EasyClassification of Numbers

Which of the following statements regarding the classification and fundamental properties of numbers are mathematically correct? (Select all that apply)

  1. The sum of any rational number and any irrational number always results in an irrational number.Answer
  2. B
    The integer 00 is considered a positive number because it sits to the right of negative values on the number line.
  3. C
    The mathematical constant π\pi is exactly equal to the fraction 227\frac{22}{7}, meaning it is classified as a rational number.
  4. The number 22 is the only even prime number, while all even integers greater than 22 are composite numbers.Answer

Answer

The correct statements are that the sum of a rational and an irrational number is always irrational, and that the number 2 is the only even prime number.
The correct statements highlight foundational number properties: a rational number added to an irrational number always forms a new irrational number, and the number 2 is unique as the only even prime number in mathematics, with all other even numbers above it containing multiple divisors.

Step-by-Step Solution

1
Evaluate the closure property of rational and irrational numbers described in the first statement.
The statement is determined to be mathematically true, as combining a rational with an irrational always yields an irrational result.
To verify if the first classification rule provided is accurate.
2
Analyze the sign classification of the integer 0 as presented in the second statement.
The statement is found to be false because 0 is a neutral integer, neither positive nor negative.
To test the common misconception that 0 holds a positive value.
3
Differentiate between the exact value of the constant pi and its fractional approximations in the third statement.
The statement is deemed false because pi is fundamentally irrational, and 22/7 is only an approximation.
To address the frequent conflation of pi with its common rational substitute.
4
Determine the prime and composite nature of even integers as claimed in the fourth statement.
The statement is recognized as true since 2 is the solely existing even prime number, with all larger even integers being composite.
To confirm the parity properties of prime numbers.

Key Concept

Classification of rational vs irrational numbers, neutral integers, and prime properties.
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Topics

Classification of Numbers

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