Problem 296
Properties of addition may be investigated in relation to sets other then the set of whole numbers. Use the set of multiples of 3, {0 ,3,6,9,….} to answer the following questions, and then justify answers:
a. Is this set closed under addition?
b. Does this set have an additive identity element?
c. Is addition with this set commutative?
d. Is addition with this set associative?
Solution
a. yes
b. yes
c. yes
d. yes