a. Prove that the intersection of two equivalence relations on a nonempty set is an equivalence relation. p. Consider the equivalence relations R2 and R3 defined on Z by a R2 b if a = b (mod 2) and a R3 if a = b(mod 3). By (a), R1 = R2 N R3 is an equivalence relation on Z. Determine the distinct equivalence classes in R.
a. Prove that the intersection of two equivalence relations on a nonempty set is an equivalence relation. p. Consider the equivalence relations R2 and R3 defined on Z by a R2 b if a = b (mod 2) and a R3 if a = b(mod 3). By (a), R1 = R2 N R3 is an equivalence relation on Z. Determine the distinct equivalence classes in R.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:9.41.
a. Prove that the intersection of two equivalence relations on a nonempty set is an equivalence relation.
b. Consider the equivalence relations R2 and R3 defined on Z by a R2 b if a = b (mod 2) and a R3 if a = b (mod 3). By (a), R1 = R2 N R3 is an equivalence
relation on Z. Determine the distinct equivalence classes in R1.
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