When considering the set of all the natural numbers (ℕ), show whether the mathematical operations of addition, subtraction, multiplication and division are: (a) Associative (b) Commutative.
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(a) Since for any we conclude that the operation of addition is associative on the set of natural numbers.
Since for any we conclude that the operation of multiplication is associative on the set of natural numbers.
Since we conclude that the operation of subtraction is not associative on the set of natural numbers.
Since we conclude that the operation of division is not associative on the set of natural numbers.
(b) Since for any we conclude that the operation of addition is commutative on the set of natural numbers.
Since for any we conclude that the operation of multiplication is commutative on the set of natural numbers.
Since we conclude that the operation of subtraction is not commutative on the set of natural numbers.
Since we conclude that the operation of division is not commutative on the set of natural numbers.