Question
Which statement is true about the relationships between the number sets?(1 point)%0D%0AResponses%0D%0A%0D%0ANot all natural numbers are real numbers.%0D%0ANot all natural numbers are real numbers.%0D%0A%0D%0AAll rational numbers are also integers.%0D%0AAll rational numbers are also integers.%0D%0A%0D%0AWhole numbers include all natural numbers and 0.%0D%0AWhole numbers include all natural numbers and 0.%0D%0A%0D%0ASome irrational numbers are also integers.
Answers
GPT-4o mini
The true statement about the relationships between the number sets is:
**Whole numbers include all natural numbers and 0.**
Here's a brief explanation of why the other statements are false:
1. **Not all natural numbers are real numbers.** - This statement is false because all natural numbers are indeed real numbers.
2. **All rational numbers are also integers.** - This is false. While all integers are rational numbers, not all rational numbers are integers (for example, 1/2 is a rational number but not an integer).
3. **Some irrational numbers are also integers.** - This is false because irrational numbers cannot be integers (irrational numbers cannot be expressed as a fraction of two integers).
Therefore, the correct statement among the options is the one about whole numbers.
**Whole numbers include all natural numbers and 0.**
Here's a brief explanation of why the other statements are false:
1. **Not all natural numbers are real numbers.** - This statement is false because all natural numbers are indeed real numbers.
2. **All rational numbers are also integers.** - This is false. While all integers are rational numbers, not all rational numbers are integers (for example, 1/2 is a rational number but not an integer).
3. **Some irrational numbers are also integers.** - This is false because irrational numbers cannot be integers (irrational numbers cannot be expressed as a fraction of two integers).
Therefore, the correct statement among the options is the one about whole numbers.