(a) Given any set of seven integers, must there be at least two that have the same remainder when divided by 6? To answer this question, let A be the set of 7 distinct integers and let 8 be the set of all possible remainders that can be obtained when an integer divided by which means that 8 has 6 the integers in A to its remainder, then by the pigeonhole ✔principle, the function is not one-to-one. Therefore, for the set of integers in A, it is impossible question is yes (b) Given any set of seven integers, must there be at least two that have the same remainder when divided by 8? If the answer is yes, enter YES. If the answer is no, enter a set of seven integers, no two of which have the same remainder when divided by 8. ✔elements. Hence, if a function is constructed from A to B that relates eac for all the integers to have different remainders when divided by 6. So, the answer to the

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