which number belongs to the set of rational numbers but does not belong to the set of whole numbers?
a. -1
b. 0
c- 1
d- 2
The set of whole numbers (W) consists of all positive integers (0, 1, 2, 3, ...) and their negatives (-1, -2, -3, ...), but it does not include zero.
On the other hand, the set of rational numbers (Q) includes all whole numbers, along with fractions and decimals that can be expressed as a ratio of integers.
Option (b) 0 does not belong to the set of whole numbers. However, it does belong to the set of rational numbers since it can be expressed as 0/1. Hence, option (b) is not the correct answer.
Options (a) -1, (c) 1, and (d) 2 all belong to the set of whole numbers since they are integers. Additionally, they all belong to the set of rational numbers because they can be expressed as -1/1, 1/1, and 2/1 respectively.
Therefore, the number that belongs to the set of rational numbers but not to the set of whole numbers is not listed among the options provided.
To determine which number belongs to the set of rational numbers but does not belong to the set of whole numbers, let's first review what each set represents:
1. Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. Rational numbers include both positive and negative numbers, as well as fractions and decimals that terminate or repeat.
2. Whole numbers: These are the set of numbers {0, 1, 2, 3, ...}, which are all positive integers starting from zero.
Now, let's analyze each option:
a. -1: This number is a negative integer, which means it can be represented as -1/1. So, -1 is a rational number.
b. 0: This number is part of the set of whole numbers, but it is also a rational number. Zero can be represented as 0/1, so it is a rational number as well.
c. 1: This number is part of both the set of whole numbers and the set of rational numbers. Like the previous options, it can be expressed as 1/1, making it a rational number.
d. 2: This number is a positive integer, which means it can also be expressed as 2/1. Therefore, 2 is a rational number.
From the options provided, none of them belong only to the set of rational numbers but not to the set of whole numbers. Therefore, the answer is that there is no number in the given options that fulfills this condition.