Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all ...

Question

Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all the elements of A that belong to each set. Rational numbers

Accepted Answer

Hello, today we're going to be enumerating all the elements of M that belong to the set of rational numbers. So what we are asked to do is you want to identify all the rational numbers that are in the number set M. Now what exactly is a rational number? Well, a rational number is a number that can be expressed as a number over a number. Or in other words, rational numbers are fractions. For example, let's say we have 1/5, 1/5 is considered a rational number. Since it is in the form of a number over a number, rational numbers can also include negative fractions such as negative 4/8 and integers may also be considered rational numbers. For example, let's say we have positive five, positive five can be rewritten as 5/1 which is in the form of a rational number. So keeping this in mind, let's take a look at the elements of M. We are given negative 13, negative 16 divided by four, negative three divided by 10, negative square root, 11 02 divided by pi 19 and the square root of 18, the first elements we can cancel out will include negative square root of five pi and the square root of 18. Since these three numbers can be considered or rewritten as continuous decimals which fall under the set of irrational numbers. Now let's take a look at the first element negative 13, negative 13 is a negative integer. However, we can rewrite negative 13 as negative 13 divided by one. So that falls under the set of rational numbers. So negative 13 will be considered a rational number. Next, we have negative 16/4. For the next element, this is already in the form of a fraction. So negative 16/4 will be considered a rational number. Negative 3/10 is considered a fraction. So it falls under the set of rational numbers. Now zero can technically be considered a rational number. C zero can be rewritten as zero divided by one and zero divided by any number will always give us zero. So zero is considered a rational number. Next two divided by five is in the form of a fraction. So this will be considered a rational number. We have positive nine which is a positive integer and nine can be rewritten as nine divided by one. So nine falls under the set of rational numbers. And the final element we have is positive 1919 is a positive integer and can be rewritten as 19 divided by one. So it falls under the set of rational numbers. So the rational numbers in the set M are negative 13, negative 16 divided by four, negative three divided by 10, 0 2/5 9 and 19. And with that being said, the answer to this problem is going to be D so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all the elements of A that belong to each set. Rational numbers

Key Concepts

Rational Numbers

Set Membership and Classification

Simplification of Expressions

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