Question

are whole numbers closed under subtraction? explain

Answer 1

A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation. For example, the positive integers are closed under addition, but not under subtraction: {\displaystyle 1-2} is not a positive integer even though both 1 and 2 are positive integers. Another example is the set containing only zero, which is closed under addition, subtraction and multiplication (because {\displaystyle 0+0=0}, {\displaystyle 0-0=0}, and {\displaystyle 0\times {0}=0}).

Similarly, a set is said to be closed under a collection of operations if it is closed under each of the operations individually.

Answer 2

The whole numbers are {0,1,2,3,...} False, because you can subtract your way out of the set of whole numbers. For instance take the two whole numbers 2 and 5. If you subtract 2 - 5 you get a negative number -3, and no negative numbers are whole numbers. So you've subtracted your way out of the set of whole numbers.