Question

Which set is closed under the operation multiplication?

A.
{0, 1}

B.
{1, 2}

C.
{0, 1, 2}

D.
{1, 2, 3}

Answer 1

What do you think?

Answer 2

I'm not sure either B or C

Answer 3

What does "closed" mean?

Answer 4

I have no clue

Answer 5

I'm on my last question and I just dont get it

Answer 6

Well closed here just basically means that if you do multiplication with any of the things in the set you don't get anything outside the set. So if you have set B, you can see that 1*1=1 so that's still in the set. What about 1*2=2? That's still in the set. But 2*2=4 which is not in the set. Since 4 isn't 1 or 2 we know that this is not closed under multiplication.

So maybe that makes it more clear?

Answer 7

Kind of

Answer 8

Just look at all the sets, multiply all the members in it with other members in the set. If you get a number that's outside the set by multiplication, then it's not closed under multiplication.

So the set {1,2,3} when you multiply the numbers together, all the possible numbers you can get out of it by multiplying once are:

{1,2,3,4,6,9}