Question

For which operations is the set {0, 1} closed?

Choose all answers that are correct.

A.
multiplication

B.
division

C.
addition

D.
subtraction

Answer 1

@green_1

Answer 2

@carlyleukhardt

Answer 3

@Missiey

Answer 4

@TheEdwardsFamily

Answer 5

a

Answer 6

what else

Answer 7

@TheEdwardsFamily

Answer 8

d

Answer 9

What do you think @goopyfish908 ?

Answer 10

A and B

Answer 11

am i right, or is it a and d

Answer 12

My explaination:

0 × 0 = 0
0 × 1 = 0
1 × 1 = 1

Which means multiplication is closed under {0, 1}

1 ÷ 1 = 1
0 ÷ 1 = 0

Division is not closed under {0, 1}

1 + 1 = 2

Addition is not closed under {0, 1}

0 - 1 = -1

Subtraction is not closed under {0, 1} either



So it makes sense to only be A. Multiplication which is closed under {0, 1}
Comments (0)

Answer 13

ok

Answer 14

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

Choose all answers that are correct.

A.
0 + (–1) = –1

B.
1 + 1 = 2

C.
2 + 0 = 2

D.
2 + (–1) = 1

Answer 15

@TheEdwardsFamily

Answer 16

@Missiey

Answer 17

First, do you know what the set of whole numbers is?

Answer 18

Then, choose examples that show addition of only whole numbers.

Answer 19

huh?

Answer 20

im so confused

Answer 21

@TheEdwardsFamily

Answer 22

@carlyleukhardt

Answer 23

When a set of numbers is closed for an operation, it means that if you take any numbers form that set and do that operation, the answer is also a part of the set.

Let's do an example.
Question: Is the set {0, 1) closed for addition?
There are two elements in this set, 0 and 1.
What are all the different additions possible with these two numbers?
They are:
0 + 0
0 + 1
1 + 0
1 + 1
What are the results of the four additions above?
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 2
The first three additions have results of 0 or 1, both of which are in the set {0, 1}, but the fourth addition, 1 +1 has a result of 2. Since 2 is not in the set {0, 1}, this means the set {0, 1} is not closed for addition because there is at least one addition using elements of the set that gives a result that is not an element of the set.

Answer 24

Your problem uses only the set {0, 1}.
Then is asks if the set {0, 1} is closed for multiplication, division, addition, and subtraction.
I showed you above that the set is not closed for addition.
Now do a similar thing for the other operations.