Answer:
All whole numbers are integers.
All natural numbers are rational numbers.
All irrational numbers are dense.
Step-by-step explanation:
1) All real numbers are natural numbers. - WRONG.
Consider [tex]$ \sqrt{2} $[/tex]. This is a real number but a natural number which consists of integers [tex]$ \{1 , 2 , 3 ,. . . \} $[/tex].
2) All whole numbers are integers. - CORRECT.
Whole numbers consist of natural numbers and zero. i.e., [tex]$ \{0, 1 , 2, . . . \}[/tex]. All these numbers are integers. Hence the statement is correct.
3) All integers are whole numbers. - WRONG.
Consider [tex]$ -1 $[/tex]. This is an integer. But not a whole number.
4) All natural numbers are rational numbers - CORRECT.
All natural numbers are a subset of rational numbers.i.e., rational numbers with denominator [tex]$ 1 $[/tex] , In fact they are a subset of real numbers as well. Hence the statement is correct.
Note that the converse isn't true,
5) All irrational numbers are dense - CORRECT.
All irrational and rational numbers are dense on a real line. This basically means that for any two irrational numbers on a real line there is always another irrational number between them. This holds for true for rational numbers as well.
Answer:
2, 4, and 5
Step-by-step explanation:
Just had the question asked on ed2020. :)
