Purchase Solution

# irrational numbers

Not what you're looking for?

Indicate which of the following statements about sets under the specified operations are true. For the ones that are false, provide one counter-example.

(a) The set of irrational numbers under addition forms an abelian group.
(b) The set of complex numbers under multiplication forms a group.
(c) The set of rational numbers under multiplication and addition forms a ring.
(d) The set of rational numbers under multiplication and addition does not form a field.

##### Solution Summary

This post examines irrational numbers and other concepts.

##### Solution Preview

(a) This statement is false, as the addition of two irrational numbers does not guarantee another irrational number. Ex: (1 + √2) + (1 - √2) = 2, which is not an irrational number.

(b) The ...

##### Probability Quiz

Some questions on probability

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.