Suppose a and b are chosen from the given set and * is theindicated operation. D

Question

Suppose a and b are chosen from the given set and * is theindicated operation. Does the equation a * x = b always have aunique solution in the set? If not, give an example of an equationwith the operation that does not have a unique solution in S. a. set of even integers, addition b. set of even integers, multiplication Suppose a and b are chosen from the given set and * is theindicated operation. Does the equation a * x = b always have aunique solution in the set? If not, give an example of an equationwith the operation that does not have a unique solution in S. a. set of even integers, addition b. set of even integers, multiplication

Explanation / Answer

a. Yes, for addition over the set of integers, there isalways a unique solution in the set. (even plus even iseven) b. No, for multiplication, there is not always a uniquesolution in the set. For example, say a=2 and b=6. Then2x=6, and the solution for x is 3, which is not in the set of evenintegers.

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