True or false
____Every integer is a rational number.
____ Every Rational number is a whole number.
____ Every natural number is a whole number.
____ 3 is an element of the rational numbers.
all naturals are whole
all wholes are integers
all integers are rational
no rationals are irrational (duh)
all rationals and irrationals are real
These inclusions only go in one direction; the reverse are not true.
so see what you can do with those.
To determine whether the given statements are true or false, we need to understand the definitions of different types of numbers.
1. Every integer is a rational number: True
To prove this, we need to recall the definition of a rational number. A rational number is any number that can be written as a fraction, where the numerator and denominator are both integers, and the denominator is not zero. Since every integer can be expressed as a fraction with a denominator of 1, every integer is also a rational number.
2. Every rational number is a whole number: False
A whole number is a non-negative integer (including zero). Rational numbers include fractions, decimals, as well as negative numbers. Therefore, not every rational number is a whole number.
3. Every natural number is a whole number: True
The natural numbers are the positive integers starting from 1. Whole numbers include the natural numbers but also include zero. Thus, every natural number is also a whole number.
4. 3 is an element of the rational numbers: True
To determine if 3 is a rational number, we need to check if it can be expressed as a fraction. Since 3 can be written as 3/1, where both the numerator and the denominator are integers (3 is an integer, and 1 is also an integer), we can conclude that 3 is indeed a rational number.
In summary:
- Every integer is a rational number: True
- Every rational number is a whole number: False
- Every natural number is a whole number: True
- 3 is an element of the rational numbers: True