Question

Is the set of numbers that can be written as the product of 6 and an integer closed under subtraction?

A.
Yes, because the difference of any two multiples of 6 is equal to 6.

B.
Yes, because the difference of any two multiples of 6 is also a multiple of 6.

C.
No, and a counterexample is 6 – 6 = 0.

D.
No, and a counterexample is 6 – 18 = –12.

Answer 1

please help

Answer 2

C and D are out right? since both 0 and -12 are multiples of 6

Answer 3

We need to get an understanding of what these number look like.

>Is the set of numbers that can be written as the product of 6 and an integer closed


The integers are {...-3, -2, -1. 0, 1, 2, 3, ...}

Answer 4

6 times each of those would be:

{..., -18, -12, -6, 0, 6, 12, 18, ...}

Answer 5

any two of those numbers and subtract them, will you get an answer that is also in that set.

Answer 6

6-6 = 0

Answer 7

the difference of any two multiples of 6 is equal to 6.

12 is a multiple of 6
24 is a multiple of 6.

12 - 24 is not equal to 6. So, throw out option A. It is wrong.

Answer 8

6 - 6 = 0 which is a multiple of 6 because 0 times 6 = 0.

So, throw out option C.

Answer 9

6 - 18 = -12 but -12 is a multiple of 6 because 6 times -2 = -12.

Throw out option D

Answer 10

The answer is B because the difference of any two multiples of 6 is also a multiple of 6.

Answer 11

so its ethier one of the yeses

Answer 12

oh ok thanks

Answer 13

Well we eliminated A, C, and D

Answer 14

So that only left B

Answer 15

No problem!

Answer 16

can you help me with 4 more questions?

Answer 17

Yes

Answer 18

ok ill give you one at a time

Answer 19

Ok thanks!

Answer 20

Numbers p and q are negative integers.
Which statements are true?
Choose all 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.
p/ q is a negative integer

Answer 21

A is correct? B is wrong? C not sure. D is wrong?

Answer 22

jckick you there?

Answer 23

let's assign p and q numbers
p=3 and q=5

Answer 24

Yes

Answer 25

is
3+5 an integer?
3-5?
3*5?
3÷5?

Answer 26

well it said p and q are both going to negative

Answer 27

A.


p + q is a positive integer

TRUE! Two positive numbers added = a positive number! Always!

B.


p – q is a negative integer

Maybe not. Ie if P = 10 and q = 1,
p-q = 10-1 = +9. FALSE

C.


p • q is a positive integer

Yes. Two positive numbers multiplied together is still a positive integer
D.


is a positive integer

Answer 28

so a and c are correct?

Answer 29

Well they said negative right?

Answer 30

yeah

Answer 31

so lets try putting it p and q negative in all the operations

Answer 32

Actually wait.

Answer 33

Just compare the two statements if they match then select it.

Answer 34

what you mean?

Answer 35

c and d

Answer 36

it goes in this order..
A.
p + q is a negative integer

B.
p • q is a positive integer

C.
p – q is a negative integer

D.
p/ q is a negative integer

Answer 37

Well A is positive. so that is false

Answer 38

you sure its not a and c?

Answer 39

a negative plus a negative equals a negative

Answer 40

Numbers p and q are negative integers.

Answer 41

Oops you are right I misread it. Sorry you are right the first one is negative.

Answer 42

ok

Answer 43

Because if p = -2 + q = -2 you get - four.

Answer 44

ya

Answer 45

Ok so how about multiplication?

Answer 46

so is it a and c?

Answer 47

Tell me the rule for multiplying two negatives.

Answer 48

multipulcation well a negative times a negative or a positive times a positve you get a positive and a negative time a positive or a positive times a negative you get a negative

Answer 49

oh so b would be it too

Answer 50

two negatives make a positive

Answer 51

In multiplication.

Answer 52

yeah

Answer 53

Ok I didn't understand what you had said.

Answer 54

So yes it would be B

Answer 55

i said the same thing you said but i said it for all of them

Answer 56

ok now we see subsraction

Answer 57

Wait

Answer 58

Subtracting a negative by a negative is a positive.

Answer 59

-2--2

Answer 60

This equals 0

Answer 61

-6 - (-3)
you keep the first number then switch it to addition then change the sign of the last number so now it is -6 plus 3 and that equals -3

Answer 62

Yes correct

Answer 63

its still negative so its correct so c is also correct

Answer 64

now lets try division

Answer 65

-8/-4 = +2

Answer 66

thats wrong

Answer 67

If the 2 numbers you are multiplying or dividing
have the SAME sign (+,+ or -,-) then the result is POSITIVE

Answer 68

so its a, b, and c

Answer 69

next question

Answer 70

Correct!

Answer 71

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 72

do you know what rational numbers are?

Answer 73

Ok so if you add any two elements of a set and you ALWAYS get another element in the set, that set is closed under addition. For example

2+2=4
2+4=6
and 4 and 6 are part of the even number set.

Answer 74

so even would be correct

Answer 75

let's go through each set
a) no 5 + 2 = 7. 7 is not in the set.

b) yes

c) yes

d) 0+0=0

Answer 76

so b c and d?

Answer 77

but what are rational numbers?

Answer 78

B.
even integers

C.
rational numbers

D.
{0}

Answer 79

a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator, q, not equal to zero.

Answer 80

In easy terms A number that can be made by dividing two integers.

Answer 81

but what does that have to do with addition? so its not correct?

Answer 82

What I have posted is the correct answer.

Answer 83

Closure:

The result of adding two rational numbers is another rational number.

Answer 84

ok ill do those 3 as the answer then

Answer 85

Ok

Answer 86

Any more questions?

Answer 87

now next question

Answer 88

Ok

Answer 89

oh just 2 more left

Answer 90

Ok shoot.

Answer 91

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 92

oh and stay close attention to where it says NOT

Answer 93

Cave, in order to show closure for a set, you need to start with two elements in the set.
(Keep in mind that negative numbers are NOT in the set of Whole numbers).

So you need to look for which one starts with two whole numbers,
then ends up with something that is not a whole number

Answer 94

It's not A

Answer 95

b is correct?

Answer 96

option A shows us doing subtraction with a negative number.
Negatives are not in the set of whole numbers.
You need to start with this whole number - whole number =

Answer 97

ok

Answer 98

Yes B is correct