Good afternoon,
Below is another question that I have for Algebra 1.
Which of the following statements is false?
A. All real numbers are rational numbers.
B. Every integer is a rational number.
C. All natural numbers are integers.
D. Every whole number is a real number.
My answer. I believe the answer is C but I am not sure.
Can you please check this?
geez. C is true. So, using it to answer the question "which statement is false" is wrong.
C is true.
The natural numbers are 1,2,3, ...
The integers are ... -3,-2,-1,0,1,2,3,...
better review the sets.
To determine which statement is false, let's review the definitions of the terms involved in each statement:
1. Real numbers: These include all rational and irrational numbers. Rational numbers can be expressed as a fraction (where the numerator and denominator are both integers), while irrational numbers cannot be expressed as fractions and have a non-repeating decimal representation.
2. Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are integers. All integers are rational numbers because they can be expressed as fractions with a denominator of 1.
3. Integers: These are whole numbers (positive, negative, or zero) and their opposites.
4. Natural numbers: These are positive integers (1, 2, 3, ...).
5. Whole numbers: These are non-negative integers (0, 1, 2, ...).
Now let's analyze each statement:
A. All real numbers are rational numbers.
This statement is true. Since rational numbers are included in real numbers, it is correct to say that all real numbers are rational numbers.
B. Every integer is a rational number.
This statement is true. As explained before, all integers can be expressed as fractions with a denominator of 1, making them rational.
C. All natural numbers are integers.
This statement is true. Natural numbers are positive integers, so they are a subset of integers.
D. Every whole number is a real number.
This statement is true. Whole numbers include both positive integers and zero, which are also real numbers.
Based on the analysis, we can see that all statements are true. Therefore, none of the statements are false.