Let G = {10n+1: n Z}; that is, G is the set of integers that are...

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Let G = {10n+1: n Z}; that is, G is the set of integers that are one more than a multiple of 10. Determine with justification whether (G, ) has each of the following properties of a group. You may state without proof properties that we know are true of integers. (a) Vu, v G, u v G (closure) (b) Vu, v, w G, (u v) w = u (v w) (associativity) (c) e such that e u = u e = u, Vu G, and e E G (exists an identity) (d) Vu G, v E G such that u v = v u = e (every element has an inverse) Let G = {10n+1: n Z}; that is, G is the set of integers that are one more than a multiple of 10. Determine with justification whether (G, ) has each of the following properties of a group. You may state without proof properties that we know are true of integers. (a) Vu, v G, u v G (closure) (b) Vu, v, w G, (u v) w = u (v w) (associativity) (c) e such that e u = u e = u, Vu G, and e E G (exists an identity) (d) Vu G, v E G such that u v = v u = e (every element has an inverse)