1. An operation is defined on the set of integers by
(a) Show that is associative and commutative.
(b) Find the identity element for , verifying that the identity axiom holds.
(c) Find a formula for the inverse of an element x, verifying that the inverse axiom holds.
(a) Let .
Therefore, is associative.
Therefore, is commutative.
Therefore, 5 is the identity for .
Therefore, is the inverse of a under .
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