Question

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 1

You want to `start with` two elements in W, perform your subtraction,
and end up with something outside of that set.

In option A,
\[\Large\rm 1-(\color{red}{-2})=3\]Notice we're performing our subtraction with an alement from outside of W,
so that doesn't show us the property failing subtraction, it's not setup correctly.

Answer 2

Whole numbers are: 0, 1, 2, 3, 4, .....
Which equations show that the set of whole numbers is not closed under subtraction?
A) 1 - (-2) = 3
1 is a whole number but -2 is not.

B) 1 - 2 = -1
1 and 2 are whole numbers. After subtraction, the result is -1 which is NOT a whole number. Therefore, this equation shows that the set of whole numbers is not closed under subtraction.

Can you try C and D?

Answer 3

thanks guys