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HW 1: Closure Homework

Last updated over 1 year ago

6 questions

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Question 1

1.

Use the definitions of rational and irrational numbers to justify each statement.
\sqrt{14} is an irrational number.

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Question 2

2.

Use the definitions of rational and irrational numbers to justify each statement.
-4 is a rational number.

Question 3

3.

The difference of two rational numbers is an irrational number.
Is this true or False? Justify your answer.

Question 4

4.

The sum of two irrational numbers is always an irrational number.
Is this true or false? Justify your answer.

Question 5

5.

Irrational numbers are closed under subtraction.
Is this true or false? If false, give a counterexample.

Question 6

6.

Irrational numbers are closed under multiplication.
Is this true or false? If false, give a counterexample.