QuestionIdentify the false statement:
1. All integers are rational numbers
2. Some rational numbers are whole numbers
3. All whole numbers are natural numbers
4. All irrational numbers are real numbers
Studdy Solution
STEP 1
Assumptions1. We understand the definitions of the different types of numbers - Integers These are whole numbers that can be positive, negative, or zero. - Rational numbers These are numbers that can be expressed as a fraction where the numerator is an integer and the denominator is a non-zero integer. - Whole numbers These are all the non-negative integers, including zero. - Natural numbers These are all the positive integers, excluding zero. - Irrational numbers These are numbers that cannot be expressed as a fraction of two integers. - Real numbers These include all rational and irrational numbers.
STEP 2
Now, let's analyze each statement one by one.
The first statement is "All integers are rational numbers".To verify this, we need to check if all integers can be expressed as a fraction where the numerator is an integer and the denominator is a non-zero integer.
STEP 3
An integer can be written as a fraction by dividing it by1. For example, the integer5 can be written as the fraction5/1.So, the statement "All integers are rational numbers" is true.
STEP 4
The second statement is "Some rational numbers are whole numbers".
To verify this, we need to check if there are any rational numbers that are also whole numbers.
STEP 5
A rational number is a whole number if the denominator of the fraction is1. For example, the rational number5/1 is the whole number5.
So, the statement "Some rational numbers are whole numbers" is true.
STEP 6
The third statement is "All whole numbers are natural numbers".
To verify this, we need to check if all whole numbers are also natural numbers.
STEP 7
Whole numbers include all the non-negative integers, including zero. Natural numbers include all the positive integers, excluding zero.So, the statement "All whole numbers are natural numbers" is NOT true because whole numbers include zero while natural numbers do not.
STEP 8
The fourth statement is "All irrational numbers are real numbers".
To verify this, we need to check if all irrational numbers are also real numbers.
STEP 9
Real numbers include all rational and irrational numbers.So, the statement "All irrational numbers are real numbers" is true.
The statement that is NOT true is "All whole numbers are natural numbers".
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