1. Define a relation on R by a ~ b iff a4 – 62 = 64 – a?. (a) Show that - is an equivalence relation. (b) Determine the equivalence class [-1]. (c) Prove or disprove: Every equivalence class in R/ ~ contains exactly 2 real numbers.

1. Define a relation on R by a ~ b iff a4 – 62 = 64 – a?. (a) Show that - is an equivalence relation. (b) Determine the equivalence class [-1]. (c) Prove or disprove: Every equivalence class in R/ ~ contains exactly 2 real numbers.

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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1.
Define a relation on R by a - b iff a4 – 62 = b4 - a².
Show that - is an equivalence relation.
(b)
Determine the equivalence class [-1].
(c)
Prove or disprove: Every equivalence class in R/ ~ contains exactly 2 real numbers.

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