Which statement is true about the relationships between the number sets?
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
Some irrational numbers are also integers.
Some irrational numbers are also integers.
Whole numbers include all positive integers and negative integers.
Whole numbers include all positive integers and negative integers.
All integers are also rational numbers.
All integers are also rational numbers.
The statement "All integers are also rational numbers" is true.
Which statement is true about the relationships between the number sets?
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
Some irrational numbers are also integers.
Some irrational numbers are also integers.
Whole numbers include all positive integers and negative integers.
Whole numbers include all positive integers and negative integers.
All rational numbers are also integers
The statement "Whole numbers include all positive integers and negative integers" is true.
Which statement is true about the relationships between the number sets?
Not all natural numbers are real numbers.
Some irrational numbers are also integers.
All rational numbers are also integers
Whole numbers include all natural numbers and 0
The statement "Whole numbers include all natural numbers and 0" is true.
The statement that is true about the relationships between the number sets is:
"All integers are also rational numbers."
To determine which statement is true about the relationships between the number sets, we can break down the statements and analyze them one by one:
1. "Not all natural numbers are real numbers."
To understand this statement, we need to first define the number sets involved. Natural numbers are the set of positive whole numbers (1, 2, 3, ...), while real numbers include both rational and irrational numbers. In this case, we can see that this statement is true because not all natural numbers are irrational (such as √2) and therefore not all natural numbers are real numbers.
2. "Some irrational numbers are also integers."
Again, let's define the number sets involved. Irrational numbers are numbers that cannot be expressed as a fraction, such as √2 or π, while integers include both positive and negative whole numbers (..., -3, -2, -1, 0, 1, 2, 3, ...). This statement is false because by definition, all integers are rational numbers. Irrational numbers cannot be expressed as fractions, and integers are always capable of being expressed as fractions (e.g., -3 = -3/1).
3. "Whole numbers include all positive integers and negative integers."
In this case, let's define the number sets again. Whole numbers include zero, positive integers (1, 2, 3, ...) and negative integers (...-3, -2, -1). This statement is true because whole numbers encompass both positive and negative integers, as well as zero.
4. "All integers are also rational numbers."
As mentioned earlier, integers are numbers without any fractional or decimal parts, including both positive and negative whole numbers and zero. Rational numbers, on the other hand, can be expressed as fractions (with non-zero denominators) or as terminating or repeating decimals. Hence, this statement is true. All integers can be expressed as a fraction with a denominator of 1, making them rational numbers.
To summarize:
- Not all natural numbers are real numbers.
- Some irrational numbers are not integers.
- Whole numbers include positive and negative integers.
- All integers are rational numbers.