Question

Which sets of numbers are closed under subtraction?

Choose all answers that are correct.

A.
odd natural numbers

B.
rational numbers

C.
{0, 1}

D.
{0, 1, 2}

Answer 1

Hm... I've never heard it called "closed" under subtraction.

Answer 2

mjm

Answer 3

Basically this is saying, which set can you manipulate in a way that it maintains its elements. There's an example here:
http://www.algebraden.com/closure_property_subtraction_of_integers.htm

Answer 4

Let's take C for example:
{0, 1}
1 - 0 = 1 which is in the set, but 0-1 = -1 which is not. So this set is NOT closed under subtraction.

Answer 5

or D:
{0, 1, 2}
again 1-2 = -1, not in the set, so not closed under subtraction

Answer 6

its a b

Answer 7

What about A?
What are odd natural numbers?

Answer 8

Well, what are odd natural numbers?

Answer 9

idk and night '='

Answer 10

odd natural numbers are odd positive integers: 1, 3, 5, etc.
so 1-3 = -2 which is NOT an odd positive integer which is why this set is NOT closed under subtraction