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Difficulty: EasyClassification of Numbers

Consider the basic definitions and categories in the number system. Which of the following statements are mathematically correct? (Select all that apply)

  1. Every integer can be expressed as a rational number.Answer
  2. B
    If a natural number is not a prime number, it must be a composite number.
  3. The number 22 is the only even prime number.Answer
  4. D
    The fraction 227\frac{22}{7} is exactly equal to the irrational number π\pi.

Answer

The correct statements are that every integer is a rational number, and the number 2 is the only even prime number.
The valid statements accurately reflect mathematical definitions: integers are a subset of rational numbers because any integer can be expressed as a fraction with a denominator of 11, and 22 is structurally the only even number with exactly two divisors.

Step-by-Step Solution

1
Analyze the relationship between integers and rational numbers.
Every integer nn can be written as n1\frac{n}{1}.
To verify if an integer fits the definition of a rational number.
2
Evaluate the classification of natural numbers into prime and composite.
The number 11 is an exception, being neither prime nor composite.
To check if the binary classification of non-prime implying composite holds true for all natural numbers.
3
Examine the properties of prime numbers and parity.
The number 22 is prime, while all other even numbers are divisible by 22 and thus composite.
To confirm whether 22 is uniquely the only even prime number.
4
Compare the fraction 227\frac{22}{7} with the mathematical constant π\pi.
227\frac{22}{7} is a rational approximation, whereas π\pi is strictly irrational.
To determine if an exact equality exists between these two commonly associated values.

Key Concept

Classification of numbers into rational, irrational, prime, and composite categories, along with their fundamental properties and exceptions.
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Topics

Classification of Numbers

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