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.

Step-by-step 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.

okay wait before i answer, is this for your points on a graph?

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: