Question

Which equations show that the set of whole numbers is not closed under subtraction?

Choose all answers that are correct.

A.
1 – (–2) = 3

B.
1 – 2 = –1

C.
2 – 0 = 2

D.
2 – 4 = –2

Answer 1

@water_girl_101 @freckles @Mimi_x3

Answer 2

can someone help me?

Answer 3

Okk whole numbers are integers that are 0 and greater so its 0,1,2,3,4,5 ......

Answer 4

So which equations when you subtract do you NOT get a whole number or rather do you get a negative number?

Answer 5

a and c

Answer 6

Ok so A and C we subtracted and still have a whole number or rather we still have a positive number
We wanna find an equation where we subtract 2 whole numbers and end up with a negative integer
Additionally If you take a look in Option A we have
1 – (–2) = 3
And -2 is a negative integer and hence not even a whole number

Answer 7

so a and c is the correct answer

Answer 8

ughhh
Nope cuz its still a positive integer

Answer 9

Ok lemme try to explain again

Answer 10

so b and d

Answer 11

yes lol

Answer 12

Which sets of numbers are closed under addition?

Choose all answers that are correct.

A.
{0, 2, 5, 8}

B.
even integers

C.
rational numbers

D.
{0}

Answer 13

can someone help me with this one

Answer 14

okkk ummm I gotta run soon but i want you to attempt to solve it on your own

Answer 15

So closed under addition means
If you added the values in each set then you still will get a value within that set
So lets take the set {0}
If you add 0+0=0
Since 0 is in the set then we can conclude that the set {0} is closed under addition

Answer 16

i think it is a d and b

Answer 17

Lets look at the set " all even integers"
So an even number is represented by 2k where k is an integer
so for instance when k=1 we have 2*1=2
When k=2 we have 2*2=4
so basically 2k represents all even functions
so 2k+2k=4k=2(2k)
so we can conclude that all even integers are closed under addition

Answer 18

am I corrrect about a d and b

Answer 19

yes I am

Answer 20

ok good

Answer 21

Ok so I dont have time to explain rational numbers cuz I am running out but a rational number is closed under addition

Answer 22

so its not a d and b

Answer 23

Lemme get @freckles to help you

Answer 24

@freckles it offfline

Answer 25

ok so basically a is the only one that isnt closed under addition
The rest are

Answer 26

hello

Answer 27

is this the question you are looking at:
"Which sets of numbers are closed under addition?

Choose all answers that are correct.

A.
{0, 2, 5, 8}

B.
even integers

C.
rational numbers

D.
{0}"

Answer 28

A) we can look at all the possibilities or we can try to find a counterexample to it being closed...(you know something showing that it is not false)
or let's look at all the possibilities
when you add any of the following, do you get a number inside the set {0,2,5,8} always:
0+0=?
0+2=?
0+5=?
0+8=?
2+2=?
2+0=?
2+5=?
2+8=?
5+0=?
5+2=?
5+5=?
5+8=?
8+0=?
8+2=?
8+5=?
8+8=?
as soon as you run into a sum that is not an element of {0,2,5,8} you know the set {0,2,5,8} will not be closed under addition

so what do you think about {0,2,5,8}
closed or not closed under addition?

Answer 29

i think the answer is even integers and rational numbers

Answer 30

what about the set just containing 0
0+0 's sum is an element of {0} is it not?

Answer 31

or it could be just a

Answer 32

why do you think a?

Answer 33

so it is b and c

Answer 34

think about the sums I mentioned above
for example is 2+8 an element {0,2,5,8}

Answer 35

no

Answer 36

so A is definitely not closed under addition

Answer 37

let's think about the even integers
2a is even for any integer a
2i is even for any integer i

what about the sum of 2a and 2i
2a+2i=2(a+i)
what does this say a bout the set of even integers under addition ?

Answer 38

yes

Answer 39

yes the set of even integers is totally closed under addition

Answer 40

now let's move on to the rationals
m/n and c/b are elements of the rationals (Assuming of course n and b are not zero you know since we can not divide by 0 and also m,n,c,b are integers )

so what happens when we add m/n and c/b

Answer 41

\[\frac{m}{n}+\frac{c}{b}=\frac{m}{n} \cdot \frac{b}{b}+\frac{c}{b} \cdot \frac{n}{n}=\frac{mb+cn}{nb}\]

Answer 42

if m,n,c,b are integers then is mb+cn an integer?

Answer 43

I will give you a hint the set of integers is closed under addition and multiplication

Answer 44

so it is c and d

Answer 45

or b and c

Answer 46

I thought you agreed with me that the set of even integers was closed under addition

we are now talking about the rationals
an element of the rationals looks like m/n or you can say c/b
where m,n,c,b are integers (and n and b are not 0)
we are adding m/n and c/b to see if the set of rationals is closed under addition
the rationals are numbers that can be written as a fraction where the numerator and denominator (not 0) are integer numbers

Answer 47

that is why I asked you to tell me if the sum of m/n and c/b 's numerator was an integer
then I was going to ask about the denominator

Answer 48

\[\frac{m}{n}+\frac{c}{b}=\frac{mb+cn}{nb}\]
I gave you the hint that the set of integers is closed under addition and multiplication which means both mb+cn and nb are integers
which means m/n+c/b is an element of the rationals
which means the set of rationals is closed under addition

Answer 49

and we already discussed the last choice
{0}
0+0 is definitely an element of {0}

Answer 50

so b and c are correct or is it b and d

Answer 51

I'm confused. Which of my explanations are you having trouble with?

Answer 52

And why do you assume you have only 2 choices of the 4 that are correct

Answer 53

again 2a+2i=2(a+i) which is still an even number
and m/n+c/b=(mb+nc)/nb where both mb+nc and nb are integers (where nb is not zero)
so m/n+c/b is still rational
0+0 is an element of 0

and finally
2+8 is not an element of {0,2,5,8}

Answer 54

is an element of {0}

Answer 55

so it it is b c and d

Answer 56

yes do you understand why ?

Answer 57

if not can you please tell me which of my explanations doesn't make sense?

Answer 58

yes

Answer 59

Numbers p and q are negative integers.

Which statements are always true?

Choose all answers that are correct.

A.
p + q is a negative integer

B.
p • q is a positive integer

C.
p – q is a negative integer

D.
is a negative integer

Answer 60

i think this one is a and c

Answer 61

so a negative number times a negative number isn't positive ?

Answer 62

also what is -5-(-5)?

Answer 63

and I can't tell what D is

Answer 64

so is it a and c

Answer 65

yep its a and c