Determine whether the following statements are true or false. Justify your answers. (a) The set Z7...

  

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Determine whether the following statements are true or false. Justify your answers. (a) The set Z7 = {0,1,2,3,4,5,6} is a group under multiplication modulo 7. (b) (c) The relation R on Z defined by aRb if a+b=0( mod 3) is an equivalence relation. S7 has a subgroup of order 11. (d) (Z4 Z15)/((2) (3)) Z6 when (2) < Z4 and (3) Determine whether the following statements are true or false. Justify your answers. (a) The set Z7 = {0,1,2,3,4,5,6} is a group under multiplication modulo 7. (b) (c) The relation R on Z defined by aRb if a+b=0( mod 3) is an equivalence relation. S7 has a subgroup of order 11. (d) (Z4 Z15)/((2) (3)) Z6 when (2) < Z4 and (3)