Which of the following sets is not dlosed under addition?
a. natural numbers
c. integers
b. whole numbers
d. odd numbers

Odd numbers.

Step-by-step explanation:

Closed under addition means you will able to take any two numbers from whatever set is mentioned and add them to get a number in that same set.

(If I say counting numbers, I'm still talking about the natural numbers.)

So let's look at the natural numbers {1,2,3,4,5,6,...}.

1+1=2

1+2=3

1+3=4

...

6+19=25

Let a and b be counting numbers.

a+b is still going to be a counting number.

You will always get a counting number when adding two counting numbers. So the counting numbers (also known as the natural numbers) is closed under addition.

Let's skip down to odd numbers because the other sets are similar to the first.

Let's add a pair of odd numbers.

3+5=8

8 is not odd so the odd numbers are not closed under addition because we will not always get an odd number. In fact, you will never get a odd number, but the thing is you just need one example to show it is not closed.

(2k+1)+(2a+1)

2(k+a)+2

2(k+a+1) is even so adding two odds will always give you an even.

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.