Answer all the questions below for your SOB to be observed. You will be asked to explain them verbally. 1. Consider the empty relation. Is it reflexive? Symmetric? Transitive? Is it a function? 2. Consider the "greater-than or equal to" relation > defined homogeneously on natural numbers. Is it reflexive? Symmetric? Transitive? Is it an equivalence relation? 3. Give an example of a function whose inverse is also a function. 4. Consider f(x) = x³ defined as f: R R. Is f one-to-one or onto? 5. Let f(x) = x² and g(x) = x+2 where f,g : R R. Compute (fo)(x), (f o g)(x), (g o f)(x). 1/1
Answer all the questions below for your SOB to be observed. You will be asked to explain them verbally. 1. Consider the empty relation. Is it reflexive? Symmetric? Transitive? Is it a function? 2. Consider the "greater-than or equal to" relation > defined homogeneously on natural numbers. Is it reflexive? Symmetric? Transitive? Is it an equivalence relation? 3. Give an example of a function whose inverse is also a function. 4. Consider f(x) = x³ defined as f: R R. Is f one-to-one or onto? 5. Let f(x) = x² and g(x) = x+2 where f,g : R R. Compute (fo)(x), (f o g)(x), (g o f)(x). 1/1
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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I need question 2,3,4 and 5 please.
Transcribed Image Text:Notes
Exercises for SOBS
Answer all the questions below for your SOB to be observed. You will
be asked to explain them verbally.
1. Consider the empty relation. Is it reflexive? Symmetric?
Transitive? Is it a function?
2. Consider the "greater-than or equal to" relation > defined
homogeneously on natural numbers. Is it reflexive? Symmetric?
Transitive? Is it an equivalence relation?
3. Give an example of a function whose inverse is also a function.
4. Consider f(x) = x³ defined as f: R R. Is f one-to-one or onto?
5. Let f(x) = x² and g(x) = x+ 2 where f, g : R R. Compute
(fof)(x), (f o g)(x), (g o f)(x).
1/1
%D
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