Let R be a relation on a nonempty set that is a partial order. Define S...
Let R be a relation on a nonempty set that is a partial order. Define S to be complement of R unioned with the identity relation. That is, (x, y) is in S if and only if either x = y or (x, y) is not in R. Then it is impossible for S to be a partial order.
T or F?
Homework Answers
Solution
F(False)
Explanation
Let R be a set of numbers with (x, y) in R if and only if x ≤y. This is a partial order.
Then (x, y) is in S if and only if x ≥y, and this is also a partial order.
Hence, The correct answer is F(False)
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