Question

For which operations is the set {–1, 1} closed?



Choose all answers that are correct.



A.


addition


B.


subtraction


C.


multiplication


D.


division

Answer 1

Didn't get the question properly.. :(

Answer 2

:/
I'm not really sure what the logic is to solve this, I have 4 more questions.. ;-;

Answer 3

Why does it put ��������� in the brackets? O_o

Answer 4

What?

Answer 5

Okay..

Answer 6

Nevermind..
I'm guessing it's C and D because, (-1) + 1 = 0, but 0 isn't in the brackets.. And same goes for subtraction since it'll end up with -2. While Multiplication & Division have -1/1 as the product/quotient..

Answer 7

Multiplication is okay.. :)

Answer 8

Division is also looking good to me.. :)

Answer 9

I'll see if I get it correct then reply when I'm done with the other 4 questions. =D

Answer 10

What are other 4?

Answer 11

Which equations show that the set of whole numbers is closed under multiplication?



Choose all answers that are correct.



A.


–1 • –1 = 1


B.


0 • –1 = 0


C.


0 • 2 = 0


D.


2 • 1 = 2

This is the second question.

Answer 12

Whole numbers are : 0, 1, 2, ..................

Answer 13

Negative numbers don't count, correct?

Answer 14

Negative numbers are not allowed..

So, you are left with two options..

Answer 15

C
And
D?

Answer 16

Good.. :)

Answer 17

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 18

That's the third question..

Answer 19

D is for sure answer :P

Answer 20

A?

Answer 21

8 + 5 = In the set or not?

Answer 22

Oh right.... :/

Answer 23

Even integer set, when you add two even you are going to get another even.. :)

Answer 24

\(2 + 4 = 6\), \(6\) is also even.. :)

Answer 25

Ohk..

Answer 26

Are rational numbers like a/b and can't end up with 0?

Answer 27

Even Integer Set is : \(\{..... -4, -2, 0, 2, 4, 6...........\}\)

Answer 28

I did not get you.. :(

Answer 29

Hold on, lemme google rational numbers. :3
Kinda forgot what it was.

Answer 30

a/b where a and be are integers and b is not zero

Answer 31

Rational numbers contain whole number + integers.. Decimals also allowed, terminating and recurring too..

Answer 32

So is 4.5 rational? because it is 9/2 I think..?

Answer 33

yep.

Answer 34

See, 4.5, the decimal ends at 5, terminating one, it is rational..

Answer 35

Ok

Answer 36

So then C. Rational Numbers wouldn't be the answer?

Answer 37

the sum of two rational numbers is a rational number

Answer 38

He he he, I was about to ask Zarkon for confirmation.. :)

Answer 39

\[\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}\]

Answer 40

If addition of two numbers is giving you a rational number which will be in the set, then it is your answer.. :)

Answer 41

Ok

Answer 42

three answers in this..

Now what is number 4 ??

Answer 43

Numbers p and q are whole numbers.



Which statements are always true?



Choose all answers that are correct.



A.


p + q is a whole number


B.


p – q is a whole number


C.


p • q is a whole number


D.


is a whole number

Answer 44

I'm thinking that it's A, B, C

Answer 45

Since we don't know what P and Q is, it might be 6 divided by 4 or something..

Answer 46

Plus I don't think that a sum would end up with a decimal when there is 2 whole numbers..
And same goes with subtraction.

Answer 47

they are whole numbers.. :P

Answer 48

\(2 - 5 = \) whole number or not?

Answer 49

Yes, but a whole number can still contain a decimal for the quotient..

Answer 50

Ahh wasn't thinking about that.. :P

Answer 51

Addition is perfect..

Answer 52

And so is multiplication?

Answer 53

yep, good..

Answer 54

Should we head onto question 5?

Answer 55

Division and subtraction can be killed here.. :)

Answer 56

Ohk.

Answer 57

Any doubt anywhere?

Answer 58

Nope.

Answer 59

For first one, division and multiplication hold good.. :)

Answer 60

Yep.

Answer 61

Okay, good, you interacted well, I appreciate you for that.. :)

Answer 62

Question 5? :P

Answer 63

Still?

Answer 64

We only did up to question 4. :P

Answer 65

Or you have 4 without counting first one?

Answer 66

Okay, let it come.. :P

Answer 67

Is the set of multiples of 6 closed under subtraction? Explain why or provide a counterexample if not.



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 68

What about b?

Answer 69

\(0\) is also a multiple of \(6\)..

Answer 70

'cause of 2 x 3 = 6..

Answer 71

wait..

Answer 72

I thought 6 x 0 = 0?

Answer 73

What do you think? What this set is?? Can you write this set?

Answer 74

Write this set? write the set for multiples of \(6\).. :)

Answer 75

Okay.\[6 \times 1\]?

Answer 76

It has to be all multiplication right?

Answer 77

You are given a set, do you know what that set is?

Answer 78

the set they gave me was multiples of 6.. Or 2 6's..

Answer 79

The set so called "Multiples of \(6\)" is the set:
\[\{..........-18, -12, -6, 0, 6, 12, 18..........\}\]

Answer 80

Multiples of \(6\) means number which are divisible by \(6\), giving \(0\) as remainder.. :)

Answer 81

getting?

Answer 82

A little bit

Answer 83

2, 3 are factors of 6 but not the multiples of 6.. :)

Answer 84

do you know the table for 6??

Answer 85

I do

Answer 86

the numbers in the table are nothing but multiples of 6..

Answer 87

Yes.