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    Partial order proof

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    Let R ba a partial order on S, and suppose that x is a unique minimal element in S.
    a) prove that S is finite, then xRy for all s in S
    b) show that the conclusion in (a) need not be true if S is infinite

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    https://brainmass.com/math/discrete-math/partial-order-proof-187129

    Solution Preview

    Proof:
    (a) For any y in S, since R is a partial order on S, then if y is not a minimal element in S, we can find y1 in S, such that
    y1Ry; if y1 is not a minimal element in S, we can find y2 in S, such that y2Ry1; and so on. Since S is ...

    Solution Summary

    This is a discrete structures proof regarding a partial order.

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