Posted by Devan on .
which of the following properties hold for subtraction of whole numbers?
A. Closure property
B. Associative property
C. commutative property
D. identity property
There is clearly no associative nor communative property of subtraction
a-(B-c)clearly does not equal (a-b)-c
The closure property: Depends on the set you are defining, for instance, subtraction of real numbers, example 5-7=-2 is closed, as 5, 7, and -2 are all real numbers. However, if the set is defined as natural numbers, then -2 is NOT a natural number, so the property of closure of subtraction of natural numbers does not exist. So this property may or may not hold, it depends on set definition.
So now, identity propery. The identity property for addition is that if you add zero to any number, the number is unchanged. The subtraction identity is that if you subtract zero from any number, it is unchanged.