Exercise 3.10. Let R be the equivalence relation on R× R given by (x,y)R(z,t) if x-y=z-t. For each of the following functions check whether they give well-defined functions from (RR)/R to R. = X. • ƒ:R× R → R given by f((x, y)) = • g: RxR → R given by g((x, y)) = x − y. • h: R × R → R given by h((x, y)) = sin²(x) + cos²(x).
Exercise 3.10. Let R be the equivalence relation on R× R given by (x,y)R(z,t) if x-y=z-t. For each of the following functions check whether they give well-defined functions from (RR)/R to R. = X. • ƒ:R× R → R given by f((x, y)) = • g: RxR → R given by g((x, y)) = x − y. • h: R × R → R given by h((x, y)) = sin²(x) + cos²(x).
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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Transcribed Image Text:Exercise 3.10. Let R be the equivalence relation on R × R given by (x,y)R(z,t) if
x - y = z-t. For each of the following functions check whether they give well-defined
functions from (R × R)/R to R.
• f:RxR → R given by f((x, y)) = x.
● g: R × R → R given by g((x, y)) = x − y.
• h: R × R → R given by h((x, y)) = sin²(x) + cos²(x).
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