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5. For the function f : Z18 Ze defined as f(r) = 4x +1 mod 6. Consider the relation R on the set Z1s defined as zRy when f(x) f(y). Show that this relation is: (a) reflexive; (b) symmetric; (c) transitive; this will prove that R is an equivalence relation; finally (d) calculate its equivalence classes.

5. For the function f : Z18 Ze defined as f(r) = 4x +1 mod 6. Consider the relation R on the set Z1s defined as zRy when f(x) f(y). Show that this relation is: (a) reflexive; (b) symmetric; (c) transitive; this will prove that R is an equivalence relation; finally (d) calculate its equivalence classes.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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part c and d

 

5. For the function f: Z18 → Ze defined as f(r) = 4x +1 mod 6. Consider the relation R on the set Z1s defined as Ry when f(r) f(y). Show that this relation is: (a) reflexive; (b) symmetric; (c) transitive; this will prove that R is an equivalence relation; finally (d) calculate its equivalence classes.
Transcribed Image Text:5. For the function f: Z18 → Ze defined as f(r) = 4x +1 mod 6. Consider the relation R on the set Z1s defined as Ry when f(r) f(y). Show that this relation is: (a) reflexive; (b) symmetric; (c) transitive; this will prove that R is an equivalence relation; finally (d) calculate its equivalence classes.
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