Let R be a relation on positive defined as follows:
for all a, b as a member of positive , aRb if and only if a/b = 2 raised to the i for some integer i.
(a) Prove R is a equivalence relation.
(b) Find 3 members of the equivalence class of 60.
To show that R is an equivalence relation, I must show that it's reflexive,symmetric and transitive:
R is reflexive if and only if aRa:
a/a = 2 raised to the i
But we know: a/a = 1, and I don't know how to prove that R is reflexive.
R is symmetric aRb and bRa
a/b = 2 raised to the i and b/a= 2 raised to the i
We can suppose a/b = 2 raised to the i and then try to show that b/a= 2 raised to the i, but thats as far as i've gotten
when R is transitive I'm at a loss...
ALSO, i dont know how to get the equivalency class 60 when its not in the set of numbers 2 raised to the i
help...