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.
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.

Answer 1

Answer:

Not closed; closed; not closed; closed.

Step-by-step explanation:

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.

Answer 2

First is not closed. (2-6=-4)
2nd is closed
3rd is not closed (-5/-5 = +1)
4th is closed