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.

Positive integers are (closed, not closed) under subtraction.

Rational numbers are (closed, not closed) under multiplication.

Negative real numbers are (closed, not closed) under division.

Irrational numbers are (closed, not closed) under addition.

If we subtract a larger positive number from a smaller positive number, we get a negative number. This means positive integers are not closed under subtraction. Example: 1-3 = -2.

Multiplying two rational numbers will give us a rational number as an answer. This means rational numbers are closed under multiplication.

If we divide two negative numbers, we get a positive number for our answer. this means that negative real numbers are not closed under division.

Adding two irrational numbers will give us an answer that is an irrational number. This means irrational numbers are closed under addition.

codiepienagoya codiepienagoya · Answer 2 · 2021-11-01T19:46:40+01:00

Following are the calculation to the given operation:

This set is sealed since the combination of any two actual figures is also a real number. In this, the actual figures are closed whenever multiplied.
The quotient might be rational in some cases. For example, [tex]\bold{\frac{(\sqrt{18})}{(\sqrt{2})} =3.}[/tex] As a result, the set remains unfinished. During division, irrational integers are not closed.
This set is closed since the difference between any two integers is an integer. Under subtraction, integers are closed.
The set is closed because the sum of any two positive rational numbers is also a positive rational number. In addition, positive rational numbers are closed.

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