1. Consider the ring Z₁2 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, with addition and multiplication modulo 12. (a) Find all of the cosets of the ideal I = an explanation of why you have found all of the cosets. (4) in Z12. Your answer should include (b) Compute the addition and multiplication tables of the factor ring Z₁2/(4) (choosing one name for each coset).

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