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x Ry⇒xy. If R is defined over the set of all integers Z, then R is a partial-order relation. (f.) Let X and Y be finite sets. If there exists a function f: X→ Y that is one-to-one, then X ≤|Y| (g.) If a set S is countable, then its powerset P(S) is also countable.

x Ry⇒xy. If R is defined over the set of all integers Z, then R is a partial-order relation. (f.) Let X and Y be finite sets. If there exists a function f: X→ Y that is one-to-one, then X ≤|Y| (g.) If a set S is countable, then its powerset P(S) is also countable.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(e.) Consider the divides relation x Ryxy. If R is defined over the set of all integers Z, then R is a partial-order relation. (f.) Let X and Y be finite sets. If there exists a function f: X→ Y that is one-to-one, then |X|≤|Y| (g.) If a set S is countable, then its powerset P(S) is also countable. (h.) The infinite union of finite sets is countable.
Transcribed Image Text:(e.) Consider the divides relation x Ryxy. If R is defined over the set of all integers Z, then R is a partial-order relation. (f.) Let X and Y be finite sets. If there exists a function f: X→ Y that is one-to-one, then |X|≤|Y| (g.) If a set S is countable, then its powerset P(S) is also countable. (h.) The infinite union of finite sets is countable.
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