Question

Member(s) x, y of a set A are said to be incomparable iff ∉ R and ∉ R. Define a relation Incomp(R) on the set A as follows: Incomp(R) = { ∈A×A: ∉ R and ∉ R}.
(a) Let R be an irreflexive partial order. Show that Incomp(R) is reflexive and symmetric.
(b) Let R be a reflexive partial order. Show that Incomp(R) is irreflexive and symmetric.
(c) Let R be an irreflexive total order on A (e.g., the "<" relation on numbers). What is
Incomp(R)?
(d) Let R be a reflexive total order on A (e.g., the "≤" relation on numbers). What is
Incomp(R)?

Answer 1

Answer:

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Step-by-step explanation:

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