
Concept explainers
Consider
(a) natural numbers
(b) whole numbers
(c) integers
(d) rational numbers
(e) irrational numbers
(f) real numbers
(a)

Answer to Problem 1T
Solution:
The only natural number in the given set is
Explanation of Solution
Given:
The set of numbers is
Explanation:
Consider the set of numbers
The set
Hence, the only natural number in the given set is
(b)

Answer to Problem 1T
Solution:
The elements of the set that are whole numbers are 0 and
Explanation of Solution
Given:
The set of numbers is
Explanation:
Consider the set of numbers
The whole numbers consist of the set of natural number and 0. The set
Hence, the elements of the set that are whole numbers are 0 and
(c)

Answer to Problem 1T
Solution:
The integers in the given set are
Explanation of Solution
Given:
The set of numbers is
Explanation:
Consider the set of numbers
The whole numbers, their negative and zeros make up the set of integers. The set
Hence the integers in the given set are
(d)

Answer to Problem 1T
Solution:
The rational number in the given set are
Explanation of Solution
Given:
The set of numbers is
Explanation:
Consider the set of numbers
All the numbers that can be written as the quotient of two integers are rational numbers. The rational numbers are
Hence the rational number in the given set are
(e)

Answer to Problem 1T
Solution:
The elements of the set that are called irrational numbers are
Explanation of Solution
Given:
The set of numbers is
Explanation:
Consider the set of numbers
The number which are not rational are called irrational numbers. In other words, numbers which cannot be written as a quotient of two integers are called irrational numbers.
Hence the elements of the set that are called irrational numbers are
(f)

Answer to Problem 1T
Solution:
All the numbers in the set which is
Explanation of Solution
Given:
The set of numbers is
Explanation:
Consider the set of numbers
The union of the sets of rational and irrational numbers are called real numbers.
Hence all the numbers in the set which is
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