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Select all of the following statements that are true. All real numbers are natural numbers. All whole numbers are integers. All integers are whole numbers. All natural numbers are rational numbers.

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ANSWER

2. All whole numbers are integers.

4. All natural numbers are rational numbers.



EXPLANATION

1. All real numbers are natural numbers
FALSE

[tex] - 2[/tex]

is a real number but it is not a natural number.




2. All whole numbers are integers.

TRUE.

The set whole numbers is a subset of the set of integers.


3. All integers are whole numbers.

FALSE

[tex] - 2[/tex]
is an integer, but it is not a whole number.


4. All natural numbers are rational numbers.

TRUE

The set of natural numbers is a subset of the set of rational numbers.

Using the number sets, it is found that the correct statements are:

  • All whole numbers are integers.
  • All natural numbers are rational numbers.

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  • Whole numbers: Also called natural, set of numbers including all positive numbers and 0, so: {0,1,2,...}
  • Integer numbers: Number without decimals, that can be positive of negative, so: {...,-2,-1,0,1,2,....}
  • Rational numbers: Integer plus decimals that can be represented by fractions, that is, they either have a pattern, or have a finite number of decimal digits, for example, 0, 2, 0,45(finite number of decimal digits), 0.3333(3 repeating is the pattern), 0.32344594459(4459 repeating is the pattern).
  • Irrational numbers: Decimal numbers that are not represented by patterns, that is, for example, 0.1033430290339.
  • Real numbers: Rational plus irrational.

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Statement 1: All real numbers are natural numbers.

Real numbers include decimals, for example, so this statement is false.

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Statement 2: All whole numbers are integers.

  • Whole numbers: {0,1,2,...}
  • Integers: whole numbers plus negatives.
  • Thus, yes, all whole numbers are integers, and this option is correct.

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Statement 3: All integers are whole numbers.

False, as integers contain negative values, which are not whole.

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Statement 4: All natural numbers are rational numbers.

  • Rational: Whole(natural + negatives) + fractions.

Thus, yes, all natural numbers are rational, and this option is correct.

A similar problem is given at https://brainly.com/question/10776450

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