equivalence relations? Determine the properties of an equivalence relation (reflexive, symmetric, transitive) that the others lack.
a) { (f,g) | f(0) = g(0) or f(1) = g(1) }
b) { (f,g) | for some C ? Z, for all x ? Z, f(x) - g(x) = C }
c) { (f,g) | f(0) = g(1) and f(1) = g(0) }
*Z is the set of integers.
I know the answers, but do not know the solving process, so please explain how to arrive at these answers:
a) Not transitive
b) Equivalence relation
c) Not reflexive or transitive
a) { (f,g) | f(0) = g(0) or f(1) = g(1) }
b) { (f,g) | for some C ? Z, for all x ? Z, f(x) - g(x) = C }
c) { (f,g) | f(0) = g(1) and f(1) = g(0) }
*Z is the set of integers.
I know the answers, but do not know the solving process, so please explain how to arrive at these answers:
a) Not transitive
b) Equivalence relation
c) Not reflexive or transitive