Posted by Devan on Monday, September 27, 2010 at 1:07pm.
There is clearly no associative nor communative property of subtraction
a-(B-c)clearly does not equal (a-b)-c
nor does
a-b=b-a
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.