1. Determine whether the following definitions of * give binary operations on gi

Question

1. Determine whether the following definitions of * give binary operations on given sets.

Justify your answers. If * defines a binary operation, decide whether it is commutative and whether it is associative.

a. On Z, define * by letting a * b = c, where c is the smallest integer greater than the sum of a and b

b. On Z, define * by letting a * b = 3^(ab)

Determine whether the following definitions of * give binary operations on given sets. Justify your answers. If * defines a binary operation, decide whether it is commutative and whether it is associative. On Z, define * by letting a * b = c, where c is the smallest integer greater than the sum of a and b. On Q, define * by letting a * b = 3ab.

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