Question 1
A) Which of the following is an irrational number?(1 point)
0
1,483,292
1427
0.100100010000...
Question 2
A) Which of the following is an example of closure?(1 point)
The equation 5β5=0 is an example of the natural numbers being closed under subtraction.
The equation 1.5+1.6=3.1 is an example of the rational numbers being closed under addition.
The equation 4β6=β2 is an example of the whole numbers being closed under subtraction.
The equation 1+0=1 is an example of the natural numbers being closed under addition.
Question 3
A) Which of the following statements about sets of numbers is true?(1 point)
All irrational numbers are integers.
All rational numbers are natural numbers.
All integers are rational numbers.
All integers are whole numbers.
Question 4
A) Without calculating, how do you know that the sum 221+331 is rational?(1 point)
Rational numbers are closed under addition, meaning that the sum of rational numbers is rational.
When adding fractions, the sum of two fractions is rational so long as both fractions are less than 1.
When adding fractions, the sum of two fractions is rational so long as both fractions are fully reduced.
The sum of any two positive numbers is rational.
Question 5
A)
Is the following statement true or false? If it is false, provide a counterexample.
The sum of two rational numbers is always rational, and the sum of two irrational numbers is always irrational.
(1 point)
The statement is false. A counterexample is the sum of the rational number 2 and the irrational number 0.3030030003....
The statement is false. A counterexample is the sum of the irrational numbers βΟ and Ο.
The statement is false. A counterexample is the sum of the rational numbers 47 and 29.
The statement is true.