Tne union of the set of rational numbers and the set of irrational numbers is
1 {whole number}
2 {real numbers}
3 {counting numbers}
4 {}
The UNION of sets consists of all elements in either set: it is a larger set than either set alone. That is enough to eliminate one of the possible answers.
pi (3.1415926535...) is an irrational number, so it is in the union set of rational and irrational numbers. Is pi a whole number? Is it a real number? Is it a counting number? If you know the meanings of those terms, the answer will be clear.
is it areal number
The correct answer is 2 {real numbers}. The union of the set of rational numbers (numbers that can be expressed as a fraction) and the set of irrational numbers (numbers that cannot be expressed as a fraction) results in the set of real numbers, which includes all rational and irrational numbers.
The union of the set of rational numbers and the set of irrational numbers is the set of real numbers.
To understand why, let's break it down:
1. Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are integers. For example, 1/2, -3/4, or 5/1 are all rational numbers.
2. Irrational numbers: These are numbers that cannot be expressed as a fraction and have non-terminating, non-repeating decimal representations. Examples of irrational numbers include √2, π (pi), and e.
Now, let's consider the union of these two sets:
- If a number is rational, it can be expressed as a fraction and therefore has a decimal representation that either terminates or repeats.
- If a number is irrational, it cannot be expressed as a fraction and its decimal representation neither terminates nor repeats.
By combining these properties, we can deduce that all rational numbers are included in the set of real numbers, while all irrational numbers are also included in the set of real numbers. Therefore, the union of the set of rational numbers and the set of irrational numbers is the set of real numbers.
So, the correct answer is 2. {real numbers}.