Asked by Aley
Let A be the set of all ordered pairs of positive integers and R be the relation defined on A where (a,b)R(c,d) means that b-a=d-c.
a)Show that R is an equivalence relation.
b)Find [(3, 5)] and [(7, 1)].
a)Show that R is an equivalence relation.
b)Find [(3, 5)] and [(7, 1)].
Answers
Answered by
MathMate
For R to be an equivalence relation, it must satisfy all the following conditions:
1) Reflexivity, i.e. (a,b)R(a,b) ∀(a,b).
2) Symmetry, i.e.
(a,b)R(c,d) => (c,d)R(a,b)
3) Transistivity, i.e.
(a,b)R(c,d) and (c,d)R(e,f) => (a,b)R(e,f).
Use the definition of R to show that all three conditions are satisfied and hence R is an equivalence relation.
1) Reflexivity, i.e. (a,b)R(a,b) ∀(a,b).
2) Symmetry, i.e.
(a,b)R(c,d) => (c,d)R(a,b)
3) Transistivity, i.e.
(a,b)R(c,d) and (c,d)R(e,f) => (a,b)R(e,f).
Use the definition of R to show that all three conditions are satisfied and hence R is an equivalence relation.
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