QUESTION 10 Consider a ring 7I/2]={a + b[/2]| a,bEZ} where addition and multiplication on ZI/2jis defined as follows: (a + b[/2]) + (c+ d[/2 ]) = (a + c) + (b+ d)[/2] (a + b[/2 ])(c+ d[ /2]) = (ac+2bd) + (ad+ bc)[/2] Prove or disprove that (a) Z[/2] is a commutative ring. (b) Z[/2] is a ring with unity. (c) Z[/2] is a field.

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