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(b) Let R and S be two equivalence relations on X. Are RnS, RUS, R \ S, also equivalence relations on X as well? If they are, then prove it. If they are not, show why they are not.

(b) Let R and S be two equivalence relations on X. Are RnS, RUS, R \ S, also equivalence relations on X as well? If they are, then prove it. If they are not, show why they are not.

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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please send handwritten solution for part b
(a) Let R and S be two posets on a set X. Are RNS, RUS, R\ S, also posets on X as well? If they are, then prove it. If they are not, show why they are not. (b) Let R and S be two equivalence relations on X. Are RNS, RUS, R \ S, also equivalence relations on X as well? If they are, then prove it. If they are not, show why they are not.
Transcribed Image Text:(a) Let R and S be two posets on a set X. Are RNS, RUS, R\ S, also posets on X as well? If they are, then prove it. If they are not, show why they are not. (b) Let R and S be two equivalence relations on X. Are RNS, RUS, R \ S, also equivalence relations on X as well? If they are, then prove it. If they are not, show why they are not.
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