# Solutions to Problem Set 2

Math 345/504

1-29-2018

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.

(b)

Therefore, 5 is the identity for .

(c)

Therefore, is the inverse of a under .

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