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Q2 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) € NxZ : n² = m} CNxZ 3. R = {(n, m) EZXZ:m-n is even} C ZX Z 4. R= {(e, y): y ER} CRX R 5. R = {(x, y) = R XR : P(x, y) is true} CRX 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.

Q2 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) € NxZ : n² = m} CNxZ 3. R = {(n, m) EZXZ:m-n is even} C ZX Z 4. R= {(e, y): y ER} CRX R 5. R = {(x, y) = R XR : P(x, y) is true} CRX 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.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.4: Relationships: Perpendicular Lines
Problem 16E: Does the relation is less than for a numbers have a reflexive property consider one number? A...
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Q2 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 ZxZ 4. R= {(e, y): y ER} CRX R 5. 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:Q2 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 ZxZ 4. R= {(e, y): y ER} CRX R 5. 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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