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Exercise 2: Relations Determine for each of the following relations R the domain dom(R). Justify your answer. 1. R = {(1, 1), (2, 2), (3, 4), (5, 9)} c Zx Z 2. R = {(n, m) ENXZ: n² = m} CNXZ 3. R = {(n, m) EZxZ:m-n is even} c Zx Z

Exercise 2: Relations Determine for each of the following relations R the domain dom(R). Justify your answer. 1. R = {(1, 1), (2, 2), (3, 4), (5, 9)} c Zx Z 2. R = {(n, m) ENXZ: n² = m} CNXZ 3. R = {(n, m) EZxZ:m-n is even} c Zx Z

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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Exercise 3: Functions For each relation R from Exercise 2, decide if R is a function or not (according to the definition given in the lecture). Prove your answer or provide a counterexample.
Transcribed Image Text:Exercise 3: Functions For each relation R from Exercise 2, decide if R is a function or not (according to the definition given in the lecture). Prove your answer or provide a counterexample.
Exercise 2: Relations Determine for each of the following relations R the domain dom(R). Justify your answer. 1. R = {(1, 1), (2, 2), (3, 4), (5, 9)} C ZX Z 2. R = {(n, m) E NXZ: n² = m} CNX Z 3. R = {(n, m) EZXZ:m-n is even} C ZxZ {(e, y): y ER} CRX R 4. R = 15. R = {(x, y) = R XR : P(x, y) is true} C R x R, where P(x, y) is the predicate y is the biggest integer such that y ≤ x ". Hint: You can use without proof that R is the union of the (disjoint) intervals [n, n + 1), indexed by n E Z.
Transcribed Image Text:Exercise 2: Relations Determine for each of the following relations R the domain dom(R). Justify your answer. 1. R = {(1, 1), (2, 2), (3, 4), (5, 9)} C ZX Z 2. R = {(n, m) E NXZ: n² = m} CNX Z 3. R = {(n, m) EZXZ:m-n is even} C ZxZ {(e, y): y ER} CRX R 4. R = 15. R = {(x, y) = R XR : P(x, y) is true} C R x R, where P(x, y) is the predicate y is the biggest integer such that y ≤ x ". Hint: You can use without proof that R is the union of the (disjoint) intervals [n, n + 1), indexed by n E Z.
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