Question

Select from the drop-down menus to correctly identify whether the given operation is closed or not closed with respect to each set of numbers.

Real numbers are Closed/Not Closed under multiplication.

Irrational numbers are Closed/Not Closed under division.

Integers are Closed/Not Closed under subtraction.

Positive rational numbers are Closed/Not Closed under addition.

Answer 1

Real numbers are Closed under multiplication.

Irrational numbers are Not Closed under division.

Integers are Closed under subtraction.

Positive rational numbers are Closed under addition

Answer 2

• Real numbers are Closed under multiplication.
• Irrational numbers are Not Closed under division.
• Integers are Closed under subtraction.
• Positive rational numbers are Closed under addition.

Explanation:

a) The product of any two real numbers is a real number, so the set is closed.

b) In some cases, the quotient may be rational. (√18)/(√2) = 3, for example. So, the set is not closed.

c) The difference of any two integers is an integer, so the set is closed.

d) The sum of any two positive rational numbers is a postive rational number, so the set is closed.