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Question: Determine whether there is a primary key for the relation in Example.
Example: Let R be the relation on Z × Z × Z consisting of all triples of integers (a, b, c) in which a, b, and c form an arithmetic progression. That is, (a, b, c) ∈ R if and only if there is an integer k such that b = a + k and c = a + 2k, or equivalently, such that b - a = k and c - b = k. Note that (1, 3, 5) ∈ R because 3 = 1 + 2 and 5 = 1 + 2 · 2, but (2, 5, 9) /∈ R because 5 - 2 = 3 while 9 - 5 = 4. This relation has degree 3 and its domains are all equal to the set of integers.
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